document_title: Tour de France records and statistics

question_text: fastest tour de france time trial in history

text: Tour de France records and statistics

text: Appearances[edit]

text: The record for most appearances is held jointly by Sylvain Chavanel, Stuart O'Grady, and Jens Voigt with 17. In light of George Hincapie's suspension for use of performance-enhancing drugs, before which he held the mark for most consecutive finishes with sixteen, having completed all but his very first, Joop Zoetemelk holds the record for the most finishes, having completed all 16 of the Tours that he started.[2]

text:
Participations
Finishes
Name
Nationality

17 (1997, 1998,[n 1] 1999–2013)
15 (1997, 1998,[n 2] 1999, 2001–2006, 2008–2013)
Stuart O'Grady
 Australia

17 (1998–2014)
14 (1998–2002, 2004, 2006–2008, 2010–2014)
Jens Voigt
 Germany

17 (2001–2017)
15 (2001–2006, 2008–2011, 2013–2017)
Sylvain Chavanel
 France

16 (1970–1973, 1975–1986)
16 (1970–1973, 1975–1986)
Joop Zoetemelk
 Netherlands

16 (2001–2009, 2011–2017)
15 (2001–2003, 2005–2009, 2011–2017)
Haimar Zubeldia
 Spain

15 (1969–1981, 1983, 1985)
15 (1969–1981, 1983, 1985)
Lucien Van Impe
 Belgium

15 (1990–1998, 2000–2004, 2006)
15 (1990–1998, 2000–2004, 2006)
Viatcheslav Ekimov
 Russia

15 (1980–1994)
13 (1981–1982, 1984–1994)
Guy Nulens
 Belgium

15 (1996–2010)
11 (1996–1997, 1999–2000, 2003–2007, 2009–2010)
Christophe Moreau
 France

15 (2003-2017)
15 (2003-2017)
Thomas Voeckler
 France

14 (1953–1966)
13 (1953–1962, 1964–1966)
André Darrigade
 France

14 (1994–2004, 2006–2008)
13 (1995–2004, 2006–2008)
Erik Zabel
 Germany

14 (1978–1985, 1987–1992)
12 (1978–1985, 1988–1990, 1992)
Sean Kelly
 Ireland

14 (1962–1976)
11 (1962–1965, 1967, 1969–1972, 1974–1976)
Raymond Poulidor
 France

14 (1908–1914, 1920–1928)
07 (1909–1914, 1921)
Jules Deloffre
 France

14 (1996–2003, 2007-2012)
13 (1997–2003, 2007-2012)[n 3]
George Hincapie
 United States

13 (1981–1988, 1989–1994)
13 (1981–1988, 1989–1994)
Phil Anderson
 Australia

13 (1969–1975, 1977–1981, 1983)
12 (1969–1975, 1977–1980, 1983)
Joaquim Agostinho
 Portugal

13 (1974–1982, 1984, 1986–1988)
11 (1974–1975, 1977–1982, 1984, 1986–1987)
Gerrie Knetemann
 Netherlands

13 (1977–1989)
11 (1977–1985, 1987, 1989)
Henk Lubberding
 Netherlands

13 (1951–1963)
10 (1951–1952, 1954, 1956–1957, 1959–1963)
Jean Dotto
 France

13 (1964–1976)
10 (1964–1965, 1967–1971, 1973–1974, 1976)
Jean-Pierre Genet
 France

13 (1979–1983, 1985–1988, 1990–1993)
09 (1979, 1981–1983, 1985, 1987–1988, 1990–1991)
Gilbert Duclos-Lassalle
 France

13 (1953–1965)
09 (1953–1955, 1957, 1959–1960, 1962–1963, 1965)
François Mahe
 France

13 (1992–1997, 1999–2005)
08 (1993–1994, 1996, 2000, 2002–2005)
Marc Wauters
 Belgium

13 (1994–2006)
07 (1995, 1997, 2000–2001, 2003, 2005–2006)
Didier Rous
 France

text: Winning margin[edit]

text: In the early years of the Tour, cyclists rode individually, and were sometimes forbidden to ride together. This led to large gaps between the winner and the number two. Since the cyclists now tend to stay together in a peloton, the margins of the winner have become smaller, as the difference usually originates from time trials, breakaways or on mountain top finishes, or from being left behind the peloton. In the table below, the eight smallest margins between the winner and the second placed cyclists at the end of the Tour are given. The largest margin, by comparison, remains that of the first Tour in 1903: 2h 49m 45s between Maurice Garin and Lucien Pothier.[3] The nine smallest margins between first and second placed riders are as follows:[4]

text:
Winning margin
Year
Opponents

8"
1989
Greg LeMond – Laurent Fignon

23"
2007
Alberto Contador – Cadel Evans

32"
2006
Óscar Pereiro – Andreas Klöden

38"
1968
Jan Janssen – Herman Van Springel

40"
1987
Stephen Roche – Pedro Delgado

48"
1977
Bernard Thévenet – Hennie Kuiper

54"
2017
Chris Froome – Rigoberto Urán

55"
1964
Jacques Anquetil – Raymond Poulidor

58"
2008
Carlos Sastre – Cadel Evans

text: Successful breakaways[edit]

text: The longest successful post-war breakaway by a single rider was by Albert Bourlon in the 1947 Tour de France. In the stage Carcassone-Luchon, he stayed away for 253 kilometres (157 mi).[5] It was one of seven breakaways longer than 200 km, the last being Thierry Marie's 234 km escape in 1991.[5] Bourlon finished 16 m 30s ahead. This is one of the biggest time gaps but not the greatest. That record belongs to José-Luis Viejo, who beat the peloton by 22 mins 50 secs in the 1976 stage Montgenèvre-Manosque.[5] He was the fourth and most recent rider to win a stage by more than 20 minutes.

text: Overall speed[edit]

text: The 2005 edition was the fastest Tour de France in history. Lance Armstrong rode 3,592.5 km in 86h 15' 02", thus realising an overall speed of 41.654 km/h, though his win was later annulled.

text: The slowest Tour de France was the edition of 1919, when Firmin Lambot's average speed was 24.056 km/h.[6]

text: Stage speeds[edit]

text: The fastest massed-start stage was in 1999 from Laval to Blois (194.5 km), won by Mario Cipollini at 50.4 km/h (31.32 mph).[7] The fastest time-trial is Rohan Dennis' stage 1 of the 2015 Tour de France in Utrecht, won at an average of 55.446 km/h (34.5 mph).[8][9] The fastest stage win was by the 2013 Orica GreenEDGE team in a team time-trial. It completed the 25 km time-trial at 57.7 km/h (35.85 mph).[10]

text: The fastest climb of Alpe d'Huez was by Marco Pantani in 1997 Tour de France at 23.1 km/h (14.35 mph).[11]

text: Stage wins per rider[edit]

text: 33 riders have won 10 or more stages (including half-stages, excluding Team Time Trials). Riders who are still active are indicated in bold. Riders with the same number of stage wins are listed alphabetically.

text:
Rank
Name
Country
Wins[12]

1
Eddy Merckx
 Belgium
34

2
Mark Cavendish
 United Kingdom
30

3
Bernard Hinault
 France
28

4
André Leducq
 France
25

5
André Darrigade
 France
22

6
Nicolas Frantz
 Luxembourg
20

7
François Faber
 Luxembourg
19

8
Jean Alavoine
 France
17

9
Jacques Anquetil
 France
16

René Le Grevès
 France
16

Charles Pélissier
 France
16

12
Freddy Maertens
 Belgium
15

13
Marcel Kittel
 Germany
14

14
Philippe Thys
 Belgium
13

Louis Trousselier
 France
13

16
Gino Bartali
 Italy
12

Mario Cipollini
 Italy
12

Miguel Indurain
 Spain
12

Robbie McEwen
 Australia
12

Erik Zabel
 Germany
12

21
Jean Aerts
 Belgium
11

Louison Bobet
 France
11

Raffaele Di Paco
 Italy
11

André Greipel
 Germany
11

25
Maurice Archambaud
 France
10

Charly Gaul
 Luxembourg
10

Walter Godefroot
 Belgium
10

Thor Hushovd
 Norway
10

Gerrie Knetemann
 Netherlands
10

Antonin Magne
 France
10

Henri Pélissier
 France
10

Jan Raas
 Netherlands
10

Joop Zoetemelk
 Netherlands
10

text: Three riders have won 8 stages in a single year:

text:
Charles Pélissier (FRA) (1930, in addition to seven 2nd places)[13]
 Eddy Merckx (BEL) (1970, 1974)[14]
 Freddy Maertens (BEL) (1976, in addition to four 2nd and two 3rd places)[15]

tag: ul

text: Mark Cavendish has the most mass finish stage wins with 30 ahead of André Darrigade and André Leducq with 22, François Faber with 19 and Eddy Merckx with 18.[16]

text: The youngest Tour de France stage winner is Fabio Battesini, who was 19 when he won one stage in the 1931 Tour de France.[17]

text: Stage wins per country[edit]

text: Riders from 33 countries have won at least one stage in the Tour de France.

text:
Country
#

 France
702

 Belgium
471

 Italy
268

 Netherlands
171

 Spain
127

 Germany
87

 Luxembourg
70

 United Kingdom
67

Country
#

  Switzerland
60

 Australia
30

 Denmark
18

 United States
18

 Norway
17

 Colombia
16

 Portugal
12

 Ireland
11

Country
#

 Russia[18]
11

 Slovakia
9

 Uzbekistan
9

 Kazakhstan
5

 Poland
5

 Austria
4

 Estonia
4

 Ukraine
4

Country
#

 Czech Republic
3

 Mexico
2

 Latvia
2

 Brazil
1

 Canada
1

 South Africa
1

 Sweden
1

 Lithuania
1

 Slovenia
1

text: Detailed table[edit]

text:
1903
5
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1904
5
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1905
11
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1906
13
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1907
14
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1908
10
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1909
7
1
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1910
11
-
1
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1911
12
1
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1912
8
5
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1913
2
10
1
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1914
7
4
-
-
-
-
2
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1919
11
2
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1920
3
12
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1921
5
9
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1922
6
8
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1923
12
2
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1924
4
4
5
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1925
1
8
5
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1926
-
12
1
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1927
6
15
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1928
13
4
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1929
10
9
-
-
1
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1930
13
3
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1931
8
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-

1932
7
6
7
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1933
9
9
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1934
20
1
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1935
13
8
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1936
13
9
-
1
1
-
2
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1937
9
10
3
-
2
4
1
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1938
8
11
5
3
-
1
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1939
17
7
-
1
-
-
2
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1947
12
2
4
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1948
6
4
11
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1949
8
5
6
-
-
-
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1950
9
2
6
-
-
-
2
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1951
6
4
5
1
2
-
1
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1952
9
3
7
2
-
-
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1953
10
1
3
5
1
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1954
15
4
-
3
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1955
9
3
2
4
2
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1956
8
4
6
-
2
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1957
17
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1958
9
2
5
1
2
-
4
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1959
12
1
4
-
1
-
1
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1960
10
5
4
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1961
12
6
3
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1962
7
8
4
1
1
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1963
8
10
1
1
2
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1964
8
7
-
4
5
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1965
3
7
5
4
4
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1966
2
8
4
5
2
3
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1967
8
6
4
1
2
1
-
2
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1968
10
10
2
2
1
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1969
3
14
3
-
1
1
-
2
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1970
5
14
5
1
2
1
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1971
4
11
3
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1972
7
15
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1973
6
7
-
2
8
-
-
3
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1974
7
15
1
2
1
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1975
3
11
4
5
1
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1976
3
12
3
7
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1977
8
6
1
5
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1978
7
5
-
9
1
1
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1979
10
4
1
8
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1980
7
4
-
11
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1981
6
10
-
7
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1982
6
5
-
6
-
-
-
-
3
1
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1983
9
3
1
5
1
-
-
1
2
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1984
12
7
-
1
1
-
-
1
-
-
-
-
-
1
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1985
6
6
-
4
2
-
-
-
-
-
1
1
-
3
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1986
6
5
3
1
5
-
-
-
2
-
-
2
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1987
7
2
1
6
4
1
-
-
-
-
-
2
1
-
1
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1988
2
-
4
8
3
1
-
1
1
-
1
-
-
1
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-

1989
4
1
2
6
1
-
-
1
1
-
-
3
-
-
1
1
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-

1990
3
2
5
6
3
1
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-

1991
5
1
6
2
2
-
-
-
-
1
-
-
-
-
-
-
3
-
2
-
-
-
-
-
-
-
-
1
-
-
-
-
-

1992
6
2
3
3
4
1
-
-
1
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1993
1
2
4
-
2
1
-
-
3
-
2
1
-
1
-
-
-
-
3
-
-
-
1
-
-
-
-
-
-
-
-
-
-

1994
4
-
5
1
2
-
-
1
-
-
3
-
-
-
-
-
-
1
2
-
-
-
-
-
-
-
2
-
-
-
-
-
-

1995
3
1
6
1
2
2
-
1
1
-
-
1
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
-

1996
4
-
3
3
-
3
-
-
3
-
3
-
-
1
-
-
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1997
6
-
7
1
1
5
-
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

1998
1
4
6
2
-
4
-
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-

1999
-
4
7
-
3
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-

2000
2
2
5
4
3
2
-
1
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

2001
4
3
-
1
1
4
-
-
-
-
-
-
-
1
-
-
1
-
-
-
-
1
-
-
1
-
-
-
-
-
-
-
-

2002
2
-
1
2
2
1
-
1
1
3
-
-
1
2
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-

2003
2
-
5
1
4
1
-
1
-
2
1
2
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-

2004
3
2
2
-
2
-
-
-
1
3
-
1
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-

2005
1
2
3
1
3
-
-
-
-
3
1
1
-
-
-
-
-
-
-
2
1
-
-
-
-
-
-
-
-
-
-
-
-

2006
3
-
1
-
4
2
1
-
-
3
1
-
2
-
-
-
1
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-

2007
2
3
3
-
1
1
1
-
2
2
2
-
1
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-

2008
3
1
-
-
6
1
1
4
1
1
-
-
2
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

2009
4
-
-
-
4
1
1
6
1
-
1
-
1
-
-
-
1
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-

2010
6
-
2
-
1
-
2
5
2
-
-
-
1
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-

2011
1
2
-
-
2
2
1
5
-
1
-
2
4
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

2012
5
-
-
-
2
3
-
7
1
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

2013
1
1
1
-
-
6
-
5
-
2
-
-
-
1
2
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

2014
2
-
5
1
-
7
-
-
-
1
-
-
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
1
-

2015
3
1
1
-
3
6
-
3
-
1
-
1
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
-
-

2016
1
2
-
2
1
2
-
7
-
1
-
-
-
1
-
-
1
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-

2017
5
-
1
2
-
5
-
1
-
2
-
-
1
1
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1

TOTAL
702
471
268
171
127
87
70
67
60
30
18
18
17
16
12
11
11
9
9
5
4
4
5
4
3
2
2
1
1
1
1
1
1

text: Stage towns[edit]

text: Some cities and towns have hosted 25 or more stage starts and finishes:

text:
Paris – 140 (most recent finish: 2017)
Bordeaux – 80 (most recent: 2010)
Pau – 69[19] (most recent: 2017)
Bagnères-de-Luchon – 58 (most recent: 2016)
Metz – 40 (most recent: 2012)
Grenoble – 39 (most recent: 2014)
Marseille – 36 (most recent: 2017)
Nice – 36 (most recent: 2013)
Perpignan – 36 (most recent: 2009)
Caen – 35 (most recent: 2006)
Briançon – 35 (most recent: 2017)
Bayonne – 32 (most recent: 2003)
Montpellier – 31 (most recent: 2016)
Nantes – 30 (most recent: 2008)
Belfort – 29 (most recent: 2000)
Brest – 28 (most recent: 2008)
L'Alpe d'Huez – 28 (most recent: 2015)
Toulouse – 25 (most recent: 2008)
Roubaix – 25 (most recent: 1994)
Saint-Étienne – 25 (most recent: 2014)

text: Notes[edit]

text:
Jump up ^ Assisted by illicit performance-enhancing drug use in the 1998 Tour de France
Jump up ^ Assisted by illicit performance-enhancing drug use in the 1998 Tour de France
Jump up ^ All appearances from 2004 to 2006 have been disqualified due to Hincapie's suspension for performance-enhancing drug use

tag: ol


document_title: Destroying angel (Bible)

question_text: what is an avenging angel in the bible

question_tokens: what is an avenging angel in the bible

root

text: Destroying angel (Bible)

text: The Destroying Angel or Angel of Death in the Hebrew Bible is an entity sent out by Yahweh on several occasions to kill enemies of the Israelites. In 2 Samuel 24:15, it kills the inhabitants of Jerusalem. In I Chronicles 21:15, the same "angel of the Lord" is seen by David to stand "between the earth and the heaven, with a drawn sword in his hand stretched out against Jerusalem." Later, the angel of the Lord kills 185,000 men of Sennacherib's Assyrian army, thereby saving Hezekiah's Jerusalem in II Kings 19:35.

tag: p

text: The angel (malak) is referred to under various terms, including Mashḥit (pron. mash-heet(h) or -kheet(h)) (Mashchit(h), מַשְׁחִית and Ha-Mashchit(h)/Ha-Mashḥit, הַמַשְׁחִית), "destroying angel" (מַלְאָך הַמַשְׁחִית, malak ha-mashḥit or in the plural מַשְׁחִיתִים, mashchitim/mashchithim/mashḥitim - "spoilers, ravagers"), Angel of the Lord, "destroyer" (מְמִיתִים, memitim - "executioners", "slayers") is found in Job 33:22 and in Proverbs 16:14 in the plural, "Messengers of death"

text: Mashchith was also used as an alternate name for one of the seven compartments of Gehenna.[1]


document_title: Standard deviation

question_text: how do you find the sd in statistics

question_tokens: how do you find the sd in statistics

text: Standard deviation

text: Basic examples[edit]

text: Sample standard deviation of metabolic rate of Northern Fulmars[edit]

text: Logan [5] gives the following example. Furness and Bryant [6] measured the resting metabolic rate for 8 male and 6 female breeding Northern fulmars. The table shows the Furness data set.

text:
Furness data set on metabolic rates of Northern fulmars

Sex
Metabolic rate
Sex
Metabolic rate

Male
525.8
Female
727.7

Male
605.7
Female
1086.5

Male
843.3
Female
1091.0

Male
1195.5
Female
1361.3

Male
1945.6
Female
1490.5

Male
2135.6
Female
1956.1

Male
2308.7

Male
2950.0

tag: table

text: The graph shows the metabolic rate for males and females. By visual inspection, it appears that the variability of the metabolic rate is greater for males than for females.

text: The sample standard deviation of the metabolic rate for the female fulmars is calculated as follows. The formula for the sample standard deviation is

text:
where

{

x

1

,

x

2

,

…
,

x

N

}

{\displaystyle \scriptstyle \{x_{1},\,x_{2},\,\ldots ,\,x_{N}\}}

 are the observed values of the sample items,

x
¯

{\displaystyle \scriptstyle {\overline {x}}}

 is the mean value of these observations, and N is the number of observations in the sample.

text: In the sample standard deviation formula, for this example, the numerator is the sum of the squared deviation of each individual animal's metabolic rate from the mean metabolic rate. The table below shows the calculation of this sum of squared deviations for the female fulmars. For females, the sum of squared deviations is 886047.09, as shown in the table.

text:
Sum of squares calculation for female fulmars

Animal
Sex
Metabolic rate
Mean
Difference from mean
Squared difference from mean

1
Female
727.7
1285.5
-557.8
311140.84

2
Female
1086.5
1285.5
-199.0
39601.00

3
Female
1091.0
1285.5
-194.5
37830.25

4
Female
1361.3
1285.5
75.8
5745.64

5
Female
1490.5
1285.5
205.0
42025.00

6
Female
1956.1
1285.5
670.6
449704.36

Mean =
1285.5

Sum of squared differences =
886047.09

text: The denominator in the sample standard deviation formula is N – 1, where N is the number of animals. In this example, there are N = 6 females, so the denominator is 6 – 1 = 5. The sample standard deviation for the female fulmars is therefore

text: For the male fulmars, a similar calculation gives a sample standard deviation of 894.37, approximately twice as large as the standard deviation for the females. The graph shows the metabolic rate data, the means (red dots), and the standard deviations (red lines) for females and males.

text: Use of the sample standard deviation implies that these 14 fulmars are a sample from a larger population of fulmars. If these 14 fulmars comprised the entire population (perhaps the last 14 surviving fulmars), then instead of the sample standard deviation, the calculation would use the population standard deviation. In the population standard deviation formula, the denominator is N instead of N-1. It is rare that measurements can be taken for an entire population, so, by default, statistical software packages calculate the sample standard deviation. Similarly, journal articles report the sample standard deviation unless otherwise specified.

text: Population standard deviation of grades of eight students[edit]

text: Suppose that the entire population of interest was eight students in a particular class. For a finite set of numbers, the population standard deviation is found by taking the square root of the average of the squared deviations of the values from their average value. The marks of a class of eight students (that is, a statistical population) are the following eight values:

text: These eight data points have the mean (average) of 5:

text: First, calculate the deviations of each data point from the mean, and square the result of each:

text: The variance is the mean of these values:

text: and the population standard deviation is equal to the square root of the variance:

text: This formula is valid only if the eight values with which we began form the complete population. If the values instead were a random sample drawn from some large parent population (for example, they were 8 marks randomly and independently chosen from a class of 2 million), then one often divides by 7 (which is n − 1) instead of 8 (which is n) in the denominator of the last formula. In that case the result of the original formula would be called the sample standard deviation. Dividing by n − 1 rather than by n gives an unbiased estimate of the variance of the larger parent population. This is known as Bessel's correction.[7]

text: Standard deviation of average height for adult men[edit]

text: If the population of interest is approximately normally distributed, the standard deviation provides information on the proportion of observations above or below certain values. For example, the average height for adult men in the United States is about 70 inches (177.8 cm), with a standard deviation of around 3 inches (7.62 cm). This means that most men (about 68%, assuming a normal distribution) have a height within 3 inches (7.62 cm) of the mean (67–73 inches (170.18–185.42 cm)) – one standard deviation – and almost all men (about 95%) have a height within 6 inches (15.24 cm) of the mean (64–76 inches (162.56–193.04 cm)) – two standard deviations. If the standard deviation were zero, then all men would be exactly 70 inches (177.8 cm) tall. If the standard deviation were 20 inches (50.8 cm), then men would have much more variable heights, with a typical range of about 50–90 inches (127–228.6 cm). Three standard deviations account for 99.7% of the sample population being studied, assuming the distribution is normal (bell-shaped). (See the 68-95-99.7 rule, or the empirical rule, for more information.)

text: Definition of population values[edit]

text: Let X be a random variable with mean value μ:

text: Here the operator E denotes the average or expected value of X. Then the standard deviation of X is the quantity

text: (derived using the properties of expected value).

text: In other words, the standard deviation σ (sigma) is the square root of the variance of X; i.e., it is the square root of the average value of (X − μ)2.

text: The standard deviation of a (univariate) probability distribution is the same as that of a random variable having that distribution. Not all random variables have a standard deviation, since these expected values need not exist. For example, the standard deviation of a random variable that follows a Cauchy distribution is undefined because its expected value μ is undefined.

text: Discrete random variable[edit]

text: In the case where X takes random values from a finite data set x1, x2, ..., xN, with each value having the same probability, the standard deviation is

text: or, using summation notation,

text: If, instead of having equal probabilities, the values have different probabilities, let x1 have probability p1, x2 have probability p2, ..., xN have probability pN. In this case, the standard deviation will be

text: Continuous random variable[edit]

text: The standard deviation of a continuous real-valued random variable X with probability density function p(x) is

text: and where the integrals are definite integrals taken for x ranging over the set of possible values of the random variable X.

text: In the case of a parametric family of distributions, the standard deviation can be expressed in terms of the parameters. For example, in the case of the log-normal distribution with parameters μ and σ2, the standard deviation is [(exp(σ2) − 1)exp(2μ + σ2)]1/2.

text: Estimation[edit]

text: One can find the standard deviation of an entire population in cases (such as standardized testing) where every member of a population is sampled. In cases where that cannot be done, the standard deviation σ is estimated by examining a random sample taken from the population and computing a statistic of the sample, which is used as an estimate of the population standard deviation. Such a statistic is called an estimator, and the estimator (or the value of the estimator, namely the estimate) is called a sample standard deviation, and is denoted by s (possibly with modifiers). However, unlike in the case of estimating the population mean, for which the sample mean is a simple estimator with many desirable properties (unbiased, efficient, maximum likelihood), there is no single estimator for the standard deviation with all these properties, and unbiased estimation of standard deviation is a very technically involved problem. Most often, the standard deviation is estimated using the corrected sample standard deviation (using N − 1), defined below, and this is often referred to as the "sample standard deviation", without qualifiers. However, other estimators are better in other respects: the uncorrected estimator (using N) yields lower mean squared error, while using N − 1.5 (for the normal distribution) almost completely eliminates bias.

text: Uncorrected sample standard deviation[edit]

text: The formula for the population standard deviation (of a finite population) can be applied to the sample, using the size of the sample as the size of the population (though the actual population size from which the sample is drawn may be much larger). This estimator, denoted by sN, is known as the uncorrected sample standard deviation, or sometimes the standard deviation of the sample (considered as the entire population), and is defined as follows:[citation needed]

text:
where

{

x

1

,

x

2

,

…
,

x

N

}

{\displaystyle \scriptstyle \{x_{1},\,x_{2},\,\ldots ,\,x_{N}\}}

 are the observed values of the sample items and

x
¯

{\displaystyle \scriptstyle {\overline {x}}}

 is the mean value of these observations, while the denominator N stands for the size of the sample: this is the square root of the sample variance, which is the average of the squared deviations about the sample mean.

text:
This is a consistent estimator (it converges in probability to the population value as the number of samples goes to infinity), and is the maximum-likelihood estimate when the population is normally distributed.[citation needed] However, this is a biased estimator, as the estimates are generally too low. The bias decreases as sample size grows, dropping off as 1/N, and thus is most significant for small or moderate sample sizes; for

N
>
75

{\displaystyle N>75}

 the bias is below 1%. Thus for very large sample sizes, the uncorrected sample standard deviation is generally acceptable. This estimator also has a uniformly smaller mean squared error than the corrected sample standard deviation.

text: Corrected sample standard deviation[edit]

text: If the biased sample variance (the second central moment of the sample, which is a downward-biased estimate of the population variance) is used to compute an estimate of the population's standard deviation, the result is

text: Here taking the square root introduces further downward bias, by Jensen's inequality, due to the square root being a concave function. The bias in the variance is easily corrected, but the bias from the square root is more difficult to correct, and depends on the distribution in question.

text: An unbiased estimator for the variance is given by applying Bessel's correction, using N − 1 instead of N to yield the unbiased sample variance, denoted s2:

text:
This estimator is unbiased if the variance exists and the sample values are drawn independently with replacement. N − 1 corresponds to the number of degrees of freedom in the vector of deviations from the mean,

(

x

1

−

x
¯

,

…
,

x

n

−

x
¯

)
.

{\displaystyle \scriptstyle (x_{1}-{\overline {x}},\;\dots ,\;x_{n}-{\overline {x}}).}

text: Taking square roots reintroduces bias (because the square root is a nonlinear function, which does not commute with the expectation), yielding the corrected sample standard deviation, denoted by s:

text:
As explained above, while s2 is an unbiased estimator for the population variance, s is still a biased estimator for the population standard deviation, though markedly less biased than the uncorrected sample standard deviation. This estimator is commonly used and generally known simply as the "sample standard deviation". The bias may still be large for small samples (N less than 10). As sample size increases, the amount of bias decreases. We obtain more information and the difference between

1
N

{\displaystyle {\frac {1}{N}}}

 and

1

N
−
1

{\displaystyle {\frac {1}{N-1}}}

 becomes smaller.

text: Unbiased sample standard deviation[edit]

text: For unbiased estimation of standard deviation, there is no formula that works across all distributions, unlike for mean and variance. Instead, s is used as a basis, and is scaled by a correction factor to produce an unbiased estimate. For the normal distribution, an unbiased estimator is given by s/c4, where the correction factor (which depends on N) is given in terms of the Gamma function, and equals:

text: This arises because the sampling distribution of the sample standard deviation follows a (scaled) chi distribution, and the correction factor is the mean of the chi distribution.

text: An approximation can be given by replacing N − 1 with N − 1.5, yielding:

text: The error in this approximation decays quadratically (as 1/N2), and it is suited for all but the smallest samples or highest precision: for n = 3 the bias is equal to 1.3%, and for n = 9 the bias is already less than 0.1%.

text: For other distributions, the correct formula depends on the distribution, but a rule of thumb is to use the further refinement of the approximation:

text: where γ2 denotes the population excess kurtosis. The excess kurtosis may be either known beforehand for certain distributions, or estimated from the data.[citation needed]

text: Confidence interval of a sampled standard deviation[edit]

text: The standard deviation we obtain by sampling a distribution is itself not absolutely accurate, both for mathematical reasons (explained here by the confidence interval) and for practical reasons of measurement (measurement error). The mathematical effect can be described by the confidence interval or CI. To show how a larger sample will make the confidence interval narrower, consider the following examples: A small population of N = 2 has only 1 degree of freedom for estimating the standard deviation. The result is that a 95% CI of the SD runs from 0.45 × SD to 31.9 × SD; the factors here are as follows:

text:
where

q

p

{\displaystyle q_{p}}

 is the p-th quantile of the chi-square distribution with k degrees of freedom, and

1
−
α

{\displaystyle 1-\alpha }

 is the confidence level. This is equivalent to the following:

text:
With k = 1,

q

0.025

=
0.000982

{\displaystyle q_{0.025}=0.000982}

 and

q

0.975

=
5.024

{\displaystyle q_{0.975}=5.024}

. The reciprocals of the square roots of these two numbers give us the factors 0.45 and 31.9 given above.

text: A larger population of N = 10 has 9 degrees of freedom for estimating the standard deviation. The same computations as above give us in this case a 95% CI running from 0.69*SD to 1.83*SD. So even with a sample population of 10, the actual SD can still be almost a factor 2 higher than the sampled SD. For a sample population N=100, this is down to 0.88*SD to 1.16*SD. To be more certain that the sampled SD is close to the actual SD we need to sample a large number of points.

text: These same formulae can be used to obtain confidence intervals on the variance of residuals from a least squares fit under standard normal theory, where k is now the number of degrees of freedom for error.

text: Identities and mathematical properties[edit]

text: The standard deviation is invariant under changes in location, and scales directly with the scale of the random variable. Thus, for a constant c and random variables X and Y:

text: The standard deviation of the sum of two random variables can be related to their individual standard deviations and the covariance between them:

text:
where

var

=

σ

2

{\displaystyle \scriptstyle \operatorname {var} \,=\,\sigma ^{2}}

 and

cov

{\displaystyle \scriptstyle \operatorname {cov} }

 stand for variance and covariance, respectively.

text: The calculation of the sum of squared deviations can be related to moments calculated directly from the data. In the following formula, the letter E is interpreted to mean expected value, i.e., mean.

text: The sample standard deviation can be computed as:

text: For a finite population with equal probabilities at all points, we have

text: This means that the standard deviation is equal to the square root of the difference between the average of the squares of the values and the square of the average value. See computational formula for the variance for proof, and for an analogous result for the sample standard deviation.

text: Interpretation and application[edit]

text: A large standard deviation indicates that the data points can spread far from the mean and a small standard deviation indicates that they are clustered closely around the mean.

text: For example, each of the three populations {0, 0, 14, 14}, {0, 6, 8, 14} and {6, 6, 8, 8} has a mean of 7. Their standard deviations are 7, 5, and 1, respectively. The third population has a much smaller standard deviation than the other two because its values are all close to 7. It will have the same units as the data points themselves. If, for instance, the data set {0, 6, 8, 14} represents the ages of a population of four siblings in years, the standard deviation is 5 years. As another example, the population {1000, 1006, 1008, 1014} may represent the distances traveled by four athletes, measured in meters. It has a mean of 1007 meters, and a standard deviation of 5 meters.

text: Standard deviation may serve as a measure of uncertainty. In physical science, for example, the reported standard deviation of a group of repeated measurements gives the precision of those measurements. When deciding whether measurements agree with a theoretical prediction, the standard deviation of those measurements is of crucial importance: if the mean of the measurements is too far away from the prediction (with the distance measured in standard deviations), then the theory being tested probably needs to be revised. This makes sense since they fall outside the range of values that could reasonably be expected to occur, if the prediction were correct and the standard deviation appropriately quantified. See prediction interval.

text: While the standard deviation does measure how far typical values tend to be from the mean, other measures are available. An example is the mean absolute deviation, which might be considered a more direct measure of average distance, compared to the root mean square distance inherent in the standard deviation.

text: Application examples[edit]

text: The practical value of understanding the standard deviation of a set of values is in appreciating how much variation there is from the average (mean).

text: Experiment, industrial and hypothesis testing[edit]

text: Standard deviation is often used to compare real-world data against a model to test the model. For example, in industrial applications the weight of products coming off a production line may need to comply with a legally required value. By weighing some fraction of the products an average weight can be found, which will always be slightly different to the long-term average. By using standard deviations, a minimum and maximum value can be calculated that the averaged weight will be within some very high percentage of the time (99.9% or more). If it falls outside the range then the production process may need to be corrected. Statistical tests such as these are particularly important when the testing is relatively expensive. For example, if the product needs to be opened and drained and weighed, or if the product was otherwise used up by the test.

text: In experimental science, a theoretical model of reality is used. Particle physics conventionally uses a standard of "5 sigma" for the declaration of a discovery.[8][not in citation given] A five-sigma level translates to one chance in 3.5 million that a random fluctuation would yield the result. This level of certainty was required in order to assert that a particle consistent with the Higgs boson had been discovered in two independent experiments at CERN,[9] and this was also the significance level leading to the declaration of the first detection of gravitational waves.[10]

text: Weather[edit]

text: As a simple example, consider the average daily maximum temperatures for two cities, one inland and one on the coast. It is helpful to understand that the range of daily maximum temperatures for cities near the coast is smaller than for cities inland. Thus, while these two cities may each have the same average maximum temperature, the standard deviation of the daily maximum temperature for the coastal city will be less than that of the inland city as, on any particular day, the actual maximum temperature is more likely to be farther from the average maximum temperature for the inland city than for the coastal one.

text: Finance[edit]

text: In finance, standard deviation is often used as a measure of the risk associated with price-fluctuations of a given asset (stocks, bonds, property, etc.), or the risk of a portfolio of assets[11] (actively managed mutual funds, index mutual funds, or ETFs). Risk is an important factor in determining how to efficiently manage a portfolio of investments because it determines the variation in returns on the asset and/or portfolio and gives investors a mathematical basis for investment decisions (known as mean-variance optimization). The fundamental concept of risk is that as it increases, the expected return on an investment should increase as well, an increase known as the risk premium. In other words, investors should expect a higher return on an investment when that investment carries a higher level of risk or uncertainty. When evaluating investments, investors should estimate both the expected return and the uncertainty of future returns. Standard deviation provides a quantified estimate of the uncertainty of future returns.

text: For example, assume an investor had to choose between two stocks. Stock A over the past 20 years had an average return of 10 percent, with a standard deviation of 20 percentage points (pp) and Stock B, over the same period, had average returns of 12 percent but a higher standard deviation of 30 pp. On the basis of risk and return, an investor may decide that Stock A is the safer choice, because Stock B's additional two percentage points of return is not worth the additional 10 pp standard deviation (greater risk or uncertainty of the expected return). Stock B is likely to fall short of the initial investment (but also to exceed the initial investment) more often than Stock A under the same circumstances, and is estimated to return only two percent more on average. In this example, Stock A is expected to earn about 10 percent, plus or minus 20 pp (a range of 30 percent to −10 percent), about two-thirds of the future year returns. When considering more extreme possible returns or outcomes in future, an investor should expect results of as much as 10 percent plus or minus 60 pp, or a range from 70 percent to −50 percent, which includes outcomes for three standard deviations from the average return (about 99.7 percent of probable returns).

text: Calculating the average (or arithmetic mean) of the return of a security over a given period will generate the expected return of the asset. For each period, subtracting the expected return from the actual return results in the difference from the mean. Squaring the difference in each period and taking the average gives the overall variance of the return of the asset. The larger the variance, the greater risk the security carries. Finding the square root of this variance will give the standard deviation of the investment tool in question.

text: Population standard deviation is used to set the width of Bollinger Bands, a widely adopted technical analysis tool. For example, the upper Bollinger Band is given as x + nσx. The most commonly used value for n is 2; there is about a five percent chance of going outside, assuming a normal distribution of returns.

text: Financial time series are known to be non-stationary series, whereas the statistical calculations above, such as standard deviation, apply only to stationary series. To apply the above statistical tools to non-stationary series, the series first must be transformed to a stationary series, enabling use of statistical tools that now have a valid basis from which to work.

text: Geometric interpretation[edit]

text: To gain some geometric insights and clarification, we will start with a population of three values, x1, x2, x3. This defines a point P = (x1, x2, x3) in R3. Consider the line L = {(r, r, r) : r ∈ R}. This is the "main diagonal" going through the origin. If our three given values were all equal, then the standard deviation would be zero and P would lie on L. So it is not unreasonable to assume that the standard deviation is related to the distance of P to L. That is indeed the case. To move orthogonally from L to the point P, one begins at the point:

text: whose coordinates are the mean of the values we started out with.

text:
[show]Derivation of

M
=
(

x
¯

,

x
¯

,

x
¯

)

{\displaystyle M=({\overline {x}},{\overline {x}},{\overline {x}})}

M

{\displaystyle M}

 is on

L

{\displaystyle L}

 therefore

M
=
(
l
,
l
,
l
)

{\displaystyle M=(l,l,l)}

 with

l
∈

R

{\displaystyle l\in {\textbf {R}}}

The line

L

{\displaystyle L}

 is to be orthogonal to the vector from

M

{\displaystyle M}

 to

P

{\displaystyle P}

. Therefore:

L
⋅
(
P
−
M
)

=
0

(
r
,
r
,
r
)
⋅
(

x

1

−
l
,

x

2

−
l
,

x

3

−
l
)

=
0

r
∗
(

x

1

−
l
+

x

2

−
l
+

x

3

−
l
)

=
0

r
∗
(

∑

i

x

i

−
3
l
)

=
0

∑

i

x

i

−
3
l

=
0

1
3

∑

i

x

i

=
l

x
¯

=
l

{\displaystyle {\begin{aligned}L\cdot (P-M)&=0\\(r,r,r)\cdot (x_{1}-l,x_{2}-l,x_{3}-l)&=0\\r*(x_{1}-l+x_{2}-l+x_{3}-l)&=0\\r*(\sum \limits _{i}x_{i}-3l)&=0\\\sum \limits _{i}x_{i}-3l&=0\\{\frac {1}{3}}\sum \limits _{i}x_{i}&=l\\{\overline {x}}&=l\end{aligned}}}

text:
A little algebra shows that the distance between P and M (which is the same as the orthogonal distance between P and the line L)

∑

i

(

x

i

−

x
¯

)

2

{\displaystyle {\sqrt {\sum \limits _{i}(x_{i}-{\overline {x}})^{2}}}}

 is equal to the standard deviation of the vector x1, x2, x3, multiplied by the square root of the number of dimensions of the vector (3 in this case.)

text: Chebyshev's inequality[edit]

text: An observation is rarely more than a few standard deviations away from the mean. Chebyshev's inequality ensures that, for all distributions for which the standard deviation is defined, the amount of data within a number of standard deviations of the mean is at least as much as given in the following table.

text:
Distance from mean
Minimum population

2

σ

{\displaystyle {\sqrt {2}}\,\sigma }

50%

2σ
75%

3σ
89%

4σ
94%

5σ
96%

6σ
97%

k
σ

{\displaystyle k\sigma }

1
−

1

k

2

{\displaystyle 1-{\frac {1}{k^{2}}}}

[12]

1

1
−
ℓ

σ

{\displaystyle {\frac {1}{\sqrt {1-\ell }}}\,\sigma }

ℓ

{\displaystyle \ell }

text: Rules for normally distributed data[edit]

text: The central limit theorem states that the distribution of an average of many independent, identically distributed random variables tends toward the famous bell-shaped normal distribution with a probability density function of

text: where μ is the expected value of the random variables, σ equals their distribution's standard deviation divided by n1/2, and n is the number of random variables. The standard deviation therefore is simply a scaling variable that adjusts how broad the curve will be, though it also appears in the normalizing constant.

text: If a data distribution is approximately normal, then the proportion of data values within z standard deviations of the mean is defined by:

text:
where

erf

{\displaystyle \scriptstyle \operatorname {erf} }

 is the error function. The proportion that is less than or equal to a number, x, is given by the cumulative distribution function:

text: If a data distribution is approximately normal then about 68 percent of the data values are within one standard deviation of the mean (mathematically, μ ± σ, where μ is the arithmetic mean), about 95 percent are within two standard deviations (μ ± 2σ), and about 99.7 percent lie within three standard deviations (μ ± 3σ). This is known as the 68-95-99.7 rule, or the empirical rule.

text: For various values of z, the percentage of values expected to lie in and outside the symmetric interval, CI = (−zσ, zσ), are as follows:

text:
Confidence
interval
Proportion within
Proportion without

Percentage
Percentage
Fraction

6999674490000000000♠0.674490σ
7001500000000000000♠50%
7001500000000000000♠50%
1 / 7000200000000000000♠2

6999994458000000000♠0.994458σ
68%
32%
1 / 3.125

1σ
7001682689492000000♠68.2689492%
7001317310508000000♠31.7310508%
1 / 7000315148720000000♠3.1514872

7000128155200000000♠1.281552σ
80%
20%
1 / 5

7000164485400000000♠1.644854σ
90%
10%
1 / 10

7000195996400000000♠1.959964σ
95%
5%
1 / 20

2σ
7001954499736000000♠95.4499736%
7000455002640000000♠4.5500264%
1 / 7001219778950000000♠21.977895

7000257582900000000♠2.575829σ
99%
1%
1 / 100

3σ
7001997300204000000♠99.7300204%
6999269979600000000♠0.2699796%
1 / 370.398

7000329052700000000♠3.290527σ
99.9%
0.1%
1 / 7003100000000000000♠1000

7000389059200000000♠3.890592σ
99.99%
0.01%
1 / 7004100000000000000♠10000

4σ
7001999936660000000♠99.993666%
6997633400000000000♠0.006334%
1 / 7004157870000000000♠15787

7000441717300000000♠4.417173σ
99.999%
0.001%
1 / 7005100000000000000♠100000

7000450000000000000♠4.5σ
99.9993204653751%
0.0006795346249%
3.4 / 7006100000000000000♠1000000 (on each side of mean)

7000489163800000000♠4.891638σ
7001999999000000000♠99.9999%
6996100000000000000♠0.0001%
1 / 7006100000000000000♠1000000

5σ
7001999999426697000♠99.9999426697%
6995573303000000000♠0.0000573303%
1 / 7006174427800000000♠1744278

7000532672399999999♠5.326724σ
7001999999900000000♠99.99999%
6995100000000000000♠0.00001%
1 / 7007100000000000000♠10000000

7000573072900000000♠5.730729σ
7001999999990000000♠99.999999%
6994100000000000000♠0.000001%
1 / 7008100000000000000♠100000000

6σ
7001999999998027000♠99.9999998027%
6993197300000000000♠0.0000001973%
1 / 7008506797346000000♠506797346

7000610941000000000♠6.109410σ
7001999999999000000♠99.9999999%
6993100000000000000♠0.0000001%
1 / 7009100000000000000♠1000000000

7000646695100000000♠6.466951σ
7001999999999900000♠99.99999999%
6992100000000000000♠0.00000001%
1 / 7010100000000000000♠10000000000

7000680650200000000♠6.806502σ
7001999999999990000♠99.999999999%
6991100000000000000♠0.000000001%
1 / 7011100000000000000♠100000000000

7σ
99.9999999997440%
6990256000000000000♠0.000000000256%
1 / 7011390682215445000♠390682215445

text: Relationship between standard deviation and mean[edit]

text: The mean and the standard deviation of a set of data are descriptive statistics usually reported together. In a certain sense, the standard deviation is a "natural" measure of statistical dispersion if the center of the data is measured about the mean. This is because the standard deviation from the mean is smaller than from any other point. The precise statement is the following: suppose x1, ..., xn are real numbers and define the function:

text: Using calculus or by completing the square, it is possible to show that σ(r) has a unique minimum at the mean:

text: Variability can also be measured by the coefficient of variation, which is the ratio of the standard deviation to the mean. It is a dimensionless number.

text: Standard deviation of the mean[edit]

text: Often, we want some information about the precision of the mean we obtained. We can obtain this by determining the standard deviation of the sampled mean. Assuming statistical independence of the values in the sample, the standard deviation of the mean is related to the standard deviation of the distribution by:

text: where N is the number of observations in the sample used to estimate the mean. This can easily be proven with (see basic properties of the variance):

text: (Statistical Independence is assumed.)

text: hence

text: Resulting in:

text:
It should be emphasized that in order to estimate the standard deviation of the mean

σ

mean

{\displaystyle \sigma _{\text{mean}}}

 it is necessary to know the standard deviation of the entire population

σ

{\displaystyle \sigma }

 beforehand. However, in most applications this parameter is unknown. For example, if a series of 10 measurements of a previously unknown quantity is performed in a laboratory, it is possible to calculate the resulting sample mean and sample standard deviation, but it is impossible to calculate the standard deviation of the mean.

text: Rapid calculation methods[edit]

text: The following two formulas can represent a running (repeatedly updated) standard deviation. A set of two power sums s1 and s2 are computed over a set of N values of x, denoted as x1, ..., xN:

text: Given the results of these running summations, the values N, s1, s2 can be used at any time to compute the current value of the running standard deviation:

text: Where N, as mentioned above, is the size of the set of values (or can also be regarded as s0).

text: Similarly for sample standard deviation,

text: In a computer implementation, as the three sj sums become large, we need to consider round-off error, arithmetic overflow, and arithmetic underflow. The method below calculates the running sums method with reduced rounding errors.[14] This is a "one pass" algorithm for calculating variance of n samples without the need to store prior data during the calculation. Applying this method to a time series will result in successive values of standard deviation corresponding to n data points as n grows larger with each new sample, rather than a constant-width sliding window calculation.

text: For k = 1, ..., n:

text: where A is the mean value.

text:
Note:

Q

1

=
0

{\displaystyle Q_{1}=0}

 since

k
−
1
=
0

{\displaystyle k-1=0}

 or

x

1

=

A

1

{\displaystyle x_{1}=A_{1}}

text: Sample variance:

text: Population variance:

text: Weighted calculation[edit]

text: When the values xi are weighted with unequal weights wi, the power sums s0, s1, s2 are each computed as:

text: And the standard deviation equations remain unchanged. Note that s0 is now the sum of the weights and not the number of samples N.

text: The incremental method with reduced rounding errors can also be applied, with some additional complexity.

text: A running sum of weights must be computed for each k from 1 to n:

text: and places where 1/n is used above must be replaced by wi/Wn:

text: In the final division,

text: and

text: or

text: where n is the total number of elements, and n' is the number of elements with non-zero weights. The above formulas become equal to the simpler formulas given above if weights are taken as equal to one.

text: History[edit]

text: The term standard deviation was first used[15] in writing by Karl Pearson[16] in 1894, following his use of it in lectures. This was as a replacement for earlier alternative names for the same idea: for example, Gauss used mean error.[17]


document_title: Legal status of tattooing in the United States

question_text: what's the age you can get a tattoo

question_tokens: what 's the age you can get a tattoo

text: In the United States, there is no federal law regulating the practice of tattooing. However, all 50 states and the District of Columbia have statutory laws requiring a person receiving a tattoo be 18 years or older. This is partially based on the legal principle that a minor cannot enter into a legal contract or otherwise render informed consent for a procedure. Most states permit a person under the age of 18 to receive a tattoo with permission of a parent or guardian, but some states outright prohibit tattooing under a certain age regardless of permission, with the exception of medical necessity (such as markings placed for radiation therapy).

text: In all jurisdictions, individual tattooists may also choose to place additional restrictions based on their own moral feelings, such as refusing any clients under a specific age even with parental consent despite it being legal, or limiting the type and/or location of where they are willing to tattoo (such as refusing any work around intimate parts of the body). They may additionally refuse to perform specific artwork, including if they merely find it inappropriate or offensive, or refuse to work on a client that they suspect may be intoxicated. Artists sometimes claim their personal business restrictions are a matter of law even when it is not true, so as to avoid arguments with clients.

text:
Legal Restrictions on Tattooing & Body Modification by State

State
Minimum Age (with parent/guardian consent)
Form of Parent/Guardian Consent
Notes & Exceptions
Intoxicated/Impaired Individuals
Area of Law/Type of Penalty
Licensing & Regulation
Relevant Statute(s) and Rules

Alabama
none specified[1]
informed written consent, signed in presence of the artist/service provider or their agent[1][2]
Ear piercing exempt from Alabama body art laws & rules.[2][3]
cannot be tattooed, branded, or pierced[1][2]
Violations of Alabama Tattoo & Body Piercing laws are a class c misdemeanor, punishable by a fine of up to $100 and/or up to 90 days imprisonment for each violation.[4]
Alabama's Department of Public Health licenses Tattoo, body piercing, & body art facilities, and sets standards for their operation.[5]
Individual tattoo artists, piercers, etc. require a permit.[2]

Ala. Code § 22-1-17A[3][6]
State Board of Health rules on Body Art Practices and Facilities.[2]

Alaska
18 (piercing excepted)[7]
parent/guardian must both give written consent and be present during the procedure[7]
Minors may be pierced with parental consent [7]
no restriction[8]

Alaska Stat. § 08.13.217[7]

Arizona
none specified[9]
parent/guardian must be physically present[9]
Minors can have their ears pierced with the written or verbal consent of a parent/guardian, can have procedures prescribed by a health care provider.[9]
no restriction[9]
Violations are a class 6 felony.[9]
There are no health regulations for tattoo shops in Arizona. [10]
Tattoos. Ariz. Rev. Stat. § 13-3721[9]

Arkansas
16[11]
parent/guardian must both give written consent and be physically present[12]
none specified[12]
cannot be tattooed, branded, or pierced.[12]

Ark. Stat. Ann. §§ 20-27-1501 et seq.[12]

California
18 (piercing excepted)[13][14]
parent/guardian must be present during procedure
Minors may have their ears pierced with parental consent.[15] They may be pierced elsewhere with parental consent, but not on their genitals or nipples. Permanent cosmetics are permitted on nipples, when done by a cosmetic technician and with parental consent.[14]
no restriction

Body Art. Cal. Health & Safety Code § 119300 to 119328[6][15]
Cal. Penal Code 653[13]

Colorado
18 Express written consent of parent or guardian[16]
parent/guardian must be present during procedure
Persons who are "noticeably impaired" cannot have body art procedures[16]

Body Artists. Colo. Rev. Stat. § 25-4-2101 to 2103[6]

Connecticut
none specified
permission of parent or guardian[17][18]
Minors may have their ears pierced without parental consent[17]
Tattooing may only be performed by physicians, or by registered nurses & technicians working under the supervision of a physician.[18]

no restrictions

Conn. Gen. Stat. §19a-92a,[6][18]
Conn. Gen. Stat. §19a-92g[6][17]

District of Columbia
18 (ear piercing excepted)[19]
written consent (for ear piercing)[19]
minors may have their ears pierced with written parental consent[19]
no restrictions[19]

Body Artists. DC Code § 47-2853.76d[6][19]

Delaware
18[20]
notarized written consent to the specific procedure[20]
none specified[20]
cannot be tattooed, branded, or body pierced[20]

Del. Code Ann. Title 11, Ch 5 §1114(a)[6][20]
Del. Code Ann. Title 16, Ch 2 §122(3)(w)[6]

Florida
16[21]
Must be accompanied by parent or guardian who can show proof of guardianship, both parent and minor must present photo ID, and a consent form must be notarized.[21]
for medical or dental purposes by a licensed physician or dentist[21]
no restriction

Fla. Stat. § 381.00787[6]
Fla. Stat. §381.0775 et seq.[6] Fla. Stat. §381.075[6]

Georgia
18 (body piercing excepted)[22]
For body piercing: prior written consent of parent/guardian[23]
Minors may have their ears pierced without parental consent[23]
Minors may be body pierced with written parental consent[23]
Physicians and Osteopaths or technicians working under their direct supervision can give minors tattoos or produce scars for "medical or cosmetic purposes."[22]
No one can be tattooed within an inch of their eye socket.[24]

no restrictions

Ga. Code § 31-40-1 to 31-40-10[6]
Ga. Code § 16-12-5[6]
Ga. Code § 16-5-71.1[6]

Hawaii
none specified[25]
written consent of parent/guardian[25]

Hawaii Rev. Stat. § 321-13[6]
Hawaii Rev. Stat. § 321-379[6]

Idaho
18[26]
Written informed consent of parent/guardian, executed in the presence of the person performing the procedure, or their agent/employee.[26]
Minors can have their ears pierced without parental consent.[6]
Piercing for medical procedures exempt.[6]

no restrictions

Idaho Code § 18-1523 (2004)[6]

Illinois
18 (body piercings excepted)[27]
Written consent of parent/guardian (for body piercings)[27]
Minors cannot be present in places where tattooing or body piercing is done except in the presence of a parent/guardian.[27]
Minors can have their ears pierced without parent/guardian consent.[27]

no restrictions

Ill. Stat. 720 §5/12-10.1[6]
Ill. Stat. 410 §54/1 t0 54/999[6]

Indiana
none specified[28]
Parent/guardian must both be present during the procedure and provide written permission.[28]
Minors may have their ears pierced without parental consent.[28]
no restrictions

Ind. Code Ann. §35-42-2-7[6][28]
Ind. Code Ann. §16-19-3-4.1[6][29]

Iowa
18[30]
n/a - minors cannot be tattooed[30]
Body piercing is not regulated by state law in Iowa, however county or city laws may regulate it.[31]
no restrictions

Iowa Code §135.37[6]
Iowa Code §135.37[6]

Kansas
16[32]
Parent/guardian must give written consent, written consent must be notarized, and the parent/guardian must be present during the procedure.[32]
Minors may have their ears pierced[33]
no restrictions

Kan. Stat. Ann. §65-1953[6]
Kan. Stat. Ann. §65-1940 to 65-1954[6]

Kentucky
16
Parent/guardian must give written, notarized consent.[34]
none (ear piercing also requires written, notarized consent).[35]

Ky. Rev. Stat. §211.760[6]
Ky. Rev. Stat. §194A.050; 211.760[6]

Louisiana
16
Parent or guardian must consent, and their presence during the procedure is required for tattoos, but not for body piercings.[36]

no restrictions

La. Rev. Stat. Ann. §14:93.2[6]
La. Rev. Stat. Ann. § 40:2831 et seq.[6]

Maine
18 (piercings excepted)[37]
For body piercings: prior legal consent of parent/guardian.[38]
Maine law does not require parent/guardian consent for ear piercing[39]
no restrictions

Me. Rev. Stat. Ann. Title 32 § 4201-4329[6]

Maryland
none specified[40]
written consent, which must be retained for 3 years.
Piercing of the ear lobe is exempt[41]
no restriction
Health Department Regulations
A license is not required, but any person performing tattooing or piercing must comply with all the relevant health code regulations[40]
COMAR 10.06.01.02 and 10.06.01.06

Massachusetts
18 (except body piercing other than genitalia)[42]
Minors cannot receive tattoo, branding, or scarification at all. For piercing of areas other than the genitalia, a parent may provide identification and sign the consent document.[42]
Physicians performing for treatment reasons and ear piercing are exempt from regulation.[42]
no restriction
County Health Department regulates body art, but all follow a model regulation set by the state.
Artists must have a permit, and establishments are subject to following specific health department regulations[42]
Model Regulations for Body Art Establishments[42]

Michigan
none specified[43]
Written, informed consent of parent/guardian. Must be executed (signed) in the presences of the person performing the procedure, or their employee.[43]

cannot be tattooed, branded, or body pierced.[43]

Mich. Comp. Laws § 333.13101 to 333.13112[44]

Minnesota
18 (piercings excepted)[45]
For piercings: presence of parent/guardian and a consent form are both required.[45]
Minors cannot be tattooed. They can be body pierced, but not in the nipples or genitals. Branding, scarification, suspension, subdermal implantation, microdermal, and tongue bifurcation are also prohibited for minors.[45]
cannot have any body art procedures.[45]

Minnesota Statutes 146B.07[45]

Mississippi
18
n/a - minors cannot be tattooed
piercing also prohibited except for the outer perimeter or lobe of the ear.
no restriction

Miss.Code Ann. §73-61

Missouri
none specified[46]
For both piercings and tattoos, parent/guardian must sign written consent in the presence of the person performing the procedure, or their employee.[46]

cannot be tattooed, branded or body pierced.[46]
violations are a misdemeanor, punishable with a fine of up to $500 (more for repeat offenses)[46]
The state director of the division of professional registration licenses all body artists, and sets rules & regulations for the operation of body art establishments.[47]
Mo. Rev. Stat. §324.520[46]

Montana
none specified[48]
Parent or guardian must give "explicit, in-person" consent.[48] Montana administrative rules also require that the parent/guardian be present throughout the procedure.[49]

cannot be tattooed or body pierced.[49]
A person who tattoos or body pierces a minor without parent/guardian consent is guilty of Unlawful transactions with children, punishable by a fine of up to $500 or six months in county jail, or both.[48]
Other violations of Montana body art laws are a misdemeanor, with punishments ranging from a fine of $50–100 for a first offense to $300 and/or 90 days in county jail for third and subsequent offense.[50]

Montana's Department of Health and Safety licenses and regulates body art establishments.[51] Local health boards may establish their own licensing and regulatory schemes in lieu of the state department's.[52]
Mont. Code Ann. §45-5-623[48]
Mont. Code Ann. §50-48-101 to 110[53]
Mont. Code Ann. §50-48-201 to 209[54]

Nebraska
none specified[55]
written consent, must be present during procedure
Piercing does not include the external parts of the ear[56]
No restrictions

Nebraska Revised Statute 38-1008, 38-1009, 38-1010, 38-1011, 38-1060, 38-10,165

Nevada
n/a[6]
n/a[6]
Nevada state law does not regulate tattoos, piercings, or other body art. Regional health districts may regulate the practice. The southern Nevada Health District, for example, does not allow minors below the age of 14 to be tattooed, and requires a parent or guardian to provide written consent and be present during the procedure for 14- to 18-year-olds. The southern Nevada district also bans tattoos on those who are under the influence of drugs or alcohol.[57]
n/a[6]

n/a[6]

New Hampshire
18 (piercings excepted)[58]
For piercings: parent/guardian must both sign written consent and be present during the procedure.
Minors cannot be tattooed or branded. They may be pierced with parent/guardian consent.[58] Minors may have their ears pierced without parent/guardian consent.[59]
no restrictions

N.H. Rev. Stat. Ann. § 314[6]

New Jersey
none specified[60]
written permission of parent/guardian is required for tattooing and body piercing.[60]
Parent/guardian must be present and sign written consent for ear piercings as well as for body piercing. Minors cannot have genital piercings even with parent/guardian consent.[61]
no restrictions
no restrictions
no restrictions
N.J. Stat. Ann. §2C:40-21
N.J.A.C. 8:27-1 et seq.
N.J. Stat. Ann. §26-1A-7[6]

New Mexico
none specified[62]
Written consent and presence during the procedure.
Medical procedures by physicians and ear piercing are exempt[63]
no restrictions
Administrative Regulations set by the Board of Barbers and Cosmetologists
All body artists are required to be licensed through the state, and are subject to regulations from the Board
Body Art Safe Practices Act. N.M. Stat. Ann. § 61-17B et seq.,[63] N.M. Administrative Code 16.36 et seq.[62]

New York
18 (piercings excepted) [64]
Minors cannot be tattooed with parent/guardian consent. For piercings: parent/guardian must give written consent, signed in presence of the body artist or body art establishment owner.[65]
Written parental consent is not required for ear piercings.[66]
no restrictions

New York Public Health Law, Article 4-A[6][65]
N.Y. Public Health Law §460-466[6]
N.Y. Penal Law § 260.21[6]

North Carolina
18 (piercings excepted)[67]
Minors cannot be tattooed, even with parent/guardian consent. "Prior consent" of parent/guardian is required for body piercings.[67]
Minors may have their ears pierced without parental consent.[67]
no restrictions

N.C. Gen. Stat. § 130A-283[68]
N.C. Gen. Stat. § 14-400[69]

North Dakota
none specified[70]
Parent/guardian must be present during the procedure and give written consent.[70]

cannot get tattoos or other body art[71]

N.D. Code §23-01-35[72]
N.D. Code §12.1-31-13[6][70]

Ohio
none specified[73]
Parent/guardian must both sign a consent form and "appear in person at the business at the time the procedure is performed."[73]
none - parent/guardian consent and presence is also required for ear piercings.[73]
no restrictions

Ohio Rev. Code Ann. §3730.01 to 3730.99[6][73]

Oklahoma
18 (piercings excepted)[74]
Minors cannot be tattooed, even with parent/guardian consent. For piercings: parent/guardian must both give written consent and be present during the procedure.[74]
Ear piercing is not governed/restricted by Oklahoma law.[74]
Scleral tattooing is illegal.[74]

cannot be tattooed.[74]

Okla. Stat. Title 21 §842.1, 842.2, 842.3[6]

Oregon
18 (piercings excepted)[75]
For piercings: parent/guardian must give written consent and present proof of identity.[76][77]
Minors can only be tattooed with the authorization of a physician.[75]
Scarification and dermal implants are prohibited[78]
Persons with sunburns or skin diseases or disorders cannot be tattooed or pierced.[75][77]
Minors cannot be pierced on the genitals or nipples, even with parent/guardian consent.[76]
Piercing on testes, deep shaft (corpus cavernosa), uvula, eyelids and sub-clavicle are all prohibited.[77]

cannot be tattooed or pierced.[75][77]
Violations of Oregon body art laws are a misdemeanor.[79]
Violations of Health Licensing Office rules are fined (various amounts).[80]

Both body artists and body art establishments are licensed by the Oregon Health Licensing Office.[81] With the assistance of a Board of Body Art practitioners, the Health Licensing Office also sets detailed rules and regulations for body art.[82]
Or. Rev. Stat. § 690.350 et seq
Or. Rev. Stat. § 690.401 to 410
Or. Rev. Stat. § 679.500[6]
Health Licensing Office Rules, especially Divisions 900, 905, 915 & 920[82]

Pennsylvania
none specified[83]
parent/guardian must both give consent and be present during the procedure.[83]

no restrictions

Pa. Cons. Stat. Title 18 § 6311[6][83]

Rhode Island
18 (piercings excepted)[84][85]
Minors cannot be tattooed.[84] For piercings: parent/guardian must both give consent and be present for the procedure.[85]

no restrictions
Tattooing a minor is a criminal offense (misdemeanor), maximum fine $300[84]
Tattooing and body art are regulated by the department of health, artists must be registered.[85]
RI Gen L § 23-1-39[85]
RI Gen L § 11-9-15[84]

South Carolina
18 (piercings excepted)[86][87]
Minors cannot be tattooed.[86] For piercings: parent/guardian must either give written, notarized consent or be present during the procedure.[87]
Head, face, and neck tattoos are illegal.[86]
cannot be tattooed or body pierced[86][88]
Under the Health Code, persons violating restrictions on tattooing and body piercing are guilty of a misdemeanor. Upon conviction, they may be fined up to $2500 or imprisoned for a year, or both.[86][87]
Tattoo and body piercing facilities are regulated by the Department of Health and Environmental Control. Tattoo facilities are licensed, body piercing facilities require a permit, and artists must be registered[89][90]
S.C. Code § 44-32-10 to 44-32-120[88]
S.C. Code § 44-34-10 to 44-34-110[91]

South Dakota
none specified[92]
Parent/guardian must sign a consent form.[92]

cannot be tattooed or pierced[93][94]
Tattooing a minor is a class 2 misdemeanor.[95]
Tattooing and Body Piercing are governed by Department of Health rules.[96] Municipalities may set stricter regulations, and have the authority to license body artists.[95]
S.D. Codified Laws Ann. §26-10-19[92]
S.D. Laws § 9-34-17[95]

Tennessee
18 (piercings excepted)[97][98]
For tattoos that cover an existing tattoo (see Notes & Exceptions): Parent/Guardian must be present during the procedure.[97]
For piercings: Parent/Guardian must give written consent, be present during the procedure.[98]

Minors over the age of sixteen may be tattooed to cover up an existing tattoo, with parent/guardian consent.[97]

Minors who lie about their age to be tattooed are guilty of a "delinquent act," are required to pay a fine of $50–$250 and serve at least 20 hours of community service.[97]
Tattooing a minor is a class a misdemeanor,[97] breach of body piercing law is a class b misdemeanor.[99]

Tattoo artists and body piercers are licensed by the state department of health, tattoo shops require a certificate from the local health department.[100][101]
Tenn. Code §§ 62-38-201-310[102]

Texas
18 (piercings excepted)[103][104]
For body piercings and for covering existing tattoos (see Notes & Exceptions): Parent/guardian must be present during procedure, sign an affidavit[103][104]
Ear piercing is exempt from body piercing statutes[105]
Minors may, with parent/guardian consent, be tattooed to cover up an existing tattoo that has offensive, gang-related, or drug-related content, or "other words, symbols, or markings that the person's parent or guardian considers would be in the best interest of the person to cover"[103]
Tongue splitting prohibited.[106]

Cannot be tattooed or pierced.[103][107]
Misrepresenting one's age to get a tattoo, or to get a piercing without parental consent, is a class B misdemeanor[103][104]
Violations of Texas tattooing & body piercing statute are a Class A misdemeanor, with each day of violation counting as a separate offense.[108]
Health Commissioner can impose a fine of up to $5000 on artists & shops for each violation[109]

Tattoo artists and body piercers must be registered with the Texas Department of Health[110] Tattoo and body piercing shops must be licensed[111]
Texas Health and Safety Code Ann. §146[112]

Utah
none specified[113]
Parent/guardian must be present during the procedure, give written permission, and provide proof of identity.[113]
Parental consent not required by law for ear piercing[113]

Tattooing or body piercing a minor is a class b misdemeanor, shops can be fined up to $1000 for each violation.[113]

Utah Code Ann. §76-10-2201[6]

Vermont
none specified[114]

Tattooists and body piercers must be registered.[114]
Vt. Stat. Ann. Title 26 §4101 to 4109[6][115]

Virginia
none specified[116]
Parent/Guardian must be present during the procedure.[116]
Virginia law does not limit minors' ability to have their ears pierced.[116]

Tattooing or body piercing a minor is a class 1 misdemeanor[116]
Tattoo artists and body piercers, as well as the operators of tattoo and body piercing establishments, are licensed by the state.[117][118]
Civic/local governments are empowered to regulate tattoo and body piercing establishments.[119]

Va. Code §54.1-700 et seq.
Va. Code §15.2-912
Va. Code § 18.2-371.3.[6]

Washington
18 (piercings excepted)[120]

cannot have tattoos, body piercings, or other body art.[121]

Wash. Code §26.28.085[120]
Wash. Code § 18.300[122]
Wash. Code § 246-145-001 to 060[123]
Wash. Code §70.54[124]

West Virginia
none specified[125]
parent/guardian must give written consent[125]

All persons receiving a tattoo must attest they are not under the influence of drugs or alcohol.[125]

Tattoo shop owners and body piercing studios must register with local board of health, and must be registered as a business with the state[126][127][128]
W. Va. Code §16-37
W. Va. Code §16-38[129]

Wisconsin
18[130]
n/a (tattooing not permitted under 18)
Physicians in the course of professional practice are exempt
no restriction
Tattooing a minor or even offering to do so is subject to a fine of up to $200
Artists must be satisfy training requirements and obtain a license from the health department. Establishments are subject to inspection and licensing[131]
Wisconsin Statutes & Annotations 948.70 and 252.235

Wyoming
none specified[132]
Verbal consent, presence during procedure.[132]
Procedures performed under the supervision of a licensed physician, and piercing of the ear, do not count as body art for this law.
no restriction[132]
Misdemeanor criminal offense, punishable by fine and prison time[132]

Wyoming Statute §14-3-107[132]


document_title: Winter Fuel Payment

question_text: when was the winter fuel payment first introduced

text: Winter Fuel Payment

text: The Winter Fuel Payment is a state benefit paid once per year in the United Kingdom to qualifying individuals. It is intended to cover the additional costs of heating over the winter months. It was introduced by the Labour government in 1997 and was first announced by Chancellor of the Exchequer Gordon Brown in his Pre-Budget Statement of that year.[1]

text: To be eligible for the benefit in a particular year, a person must be over age 60 (born before a specific qualifying date — e.g. 5 January 1952 for payments for the winter 2013-2014), and in a specified week (22-29 September 2013, for 2013-2014) must be resident in the United Kingdom and not in any of the excluded groups (prisoners, people receiving long-term free hospital care, those with certain immigration issues, and those living in care homes and receiving income-related benefits such as pension credit).[2]

text: The amount paid is greater for those aged 80 and above, and is set so that a person living alone (or with people ineligible for the payment) is paid twice as much as a person in a household where more than one person receives the payment.[3]

text: If the weather is particularly cold, a cold weather payment may also be made.

text: The Social Fund (Winter Fuel Payment) Regulations 2000 govern the system, under the Social Security Contributions and Benefits Act 1992.

text: In the winter of 2011-12, the benefit cost the government £2.1 billion and was paid to 12.7 million people.[4]


document_title: Civil Services Examination (India)

question_text: civil services exam age limit for general category

text: Civil Services Examination (India)

text: Process[edit]

text: The Civil Services Examination is based on the British Raj Era Imperial Civil Service tests, as well as the civil service tests conducted by old Indian empires such as in the Mauryan Empire and Mughal Empire. The Civil Services Examination is considered to be one of the most difficult competitive examination in India. On an average, 900,000 to 1,000,000 candidates apply every year and the number of candidates appearing to sit the preliminary examination is approximately 500,000.[2] The examination consists of the following stage. Results are published in mid-August.

text:
Stage I: Main examination - Held in October every year.
Stage II: Personality Test (interview) - held in March each year. Final results are usually announced in May .

text: The training program for the selected candidates usually commences the following September.

text: Eligibility[edit]

text: Eligibility for the examination is as follows:[1]

text: Nationality[edit]

text:
For the Indian Administrative Service and the Indian Police Service, the candidate must be a citizen of India.
For other services, the candidate must be one of the following:
A citizen of India
A citizen of Nepal or a subject of Bhutan
A person of Indian origin who has migrated from Pakistan, Myanmar, Sri Lanka, Kenya, Uganda, Tanzania, Zambia, Malawi, Zaire, Ethiopia or Vietnam with the intention of permanently settling in India

text: Education[edit]

text: All candidates must have as a minimum one of the following educational qualifications:

text:
A degree from a Central, State or a Deemed university[1]
A degree received through correspondence or distance education
A degree from an open university[3]
A qualification recognized by the Government of India as being equivalent to one of the above[1]

text: The following candidates are also eligible, but must submit proof of their eligibility from a competent authority at their institute/university at the time of the main examination, failing which they will not be allowed to attend the exam.[1]

text:
Candidates who have appeared in an examination, the passing of which would render them educationally qualified enough to satisfy one of the above points[4]
Candidates who have passed the final exam of the MBBS degree but have not yet completed an internship.
Candidates who have passed the final exam of ICAI, ICSI and ICWAI.
A degree from a private university.
A degree from any foreign university recognized by the Association of Indian Universities.

text: Age[edit]

text:
The candidate must have attained the age of 21 years and must not have attained the age of 32 years (for the General category candidate) on August 1 of the year of examination.
Prescribed age limits vary with respect to caste reservations.

text:
For Other Backward Castes (OBC) the upper age limit is35
For Scheduled Castes (SC) and Scheduled Tribes (ST), the limit is 37 years.
The upper age limit is relaxed for certain candidates who are backward with respect to other factors and differently abled[5]

text: Number of attempts[edit]

text: The number of times a candidate may attempt the exam is limited as follows:[3]

text:
General category candidates = 6.[6]
OBC category candidates = 9.
SC/ST candidates = unlimited attempts till 37 years of age.

text: Appearing to attempt one of the papers in the preliminary examination is counted as an attempt, including disqualification/ cancellation of candidature. However, applying to sit the exam but failing to attend is not counted as an attempt.[7]

text: Vacancies and Selection[edit]

text: Generally the number of vacancies varies every year. The number of candidates that pass the preliminary examination is generally 11 or 12 times the number of vacancies, and the number of candidates selected for the final interview is twice the number of vacancies. As per existing policies, reservation for SC/ST/OBC is applied to each level of the selection process.

text:
Vacancies in different years

Year

Number of candidates appeared for

Number of cadidates
called for interviews

Final
Vacancies

Prelims

Mains

2010

269036

11865

2589

1043

2011

243236

11237

2415

1001

2012

271442

12190

2674

1091

2013

3,23,949

14178

3003

1228

2014

4,51,602

16286

3308

1364

2015

4,65,882

15000*

2797

1164

2016

4,59,659

15445

2961

1209

text: List of Services[edit]

text: Following are the services which one gets on qualifying the Civil Service Examination.[8]

text: All India Services

text:
Indian Administrative Service (IAS)
Indian Police Service(IPS)
Indian Forest Service(IFS)

text: Central Services (Group A)

text:
Indian P&T Accounts and Finance Service (IP&TAFS)
Indian Audit and Accounts Service (IA&AS)
Indian Civil Accounts Service (ICAS)
Indian Corporate Law Service (ICLS)
Indian Defence Accounts Service (IDAS)
Indian Defence Estates Service (IDES)
Indian Forest Service (IFoS)
Indian Information Service (IIS)
Indian Ordnance Factories Service (IOFS)
Indian Postal Service (IPoS)
Indian Railway Accounts Service (IRAS)
Indian Railway Personnel Service (IRPS)
Indian Railway Traffic Service (IRTS)
Indian Revenue Service (IRS-IT)
Indian Revenue Service (IRS-C&CE)
Indian Trade Service (ITrS)
Railway Protection Force (RPF)

text: Group B Services

text:
Armed Forces Headquarters Civil Service (AFHCS)
Delhi, Andaman and Nicobar Islands Civil Service (DANICS)
Delhi, Andaman and Nicobar Islands Police Service (DANIPS)
Pondicherry Civil Service (PCS)
Pondicherry Police Service (PPS)

text: Preliminary[edit]

text: The pattern of the Preliminary examination up to 2010 was based on the recommendations of the Kothari Commission (1979). It included two examinations, one on general studies worth 150 marks, and the second on one of 23 optional subjects worth 300 marks. Until 2011, when it was revamped,[9] the preliminary pattern was sustained with only minor changes once every ten to fifteen years.[9]

text: From 2011 onwards, the preliminary examination, now popularly known as the Civil Services Aptitude Test (CSAT) (officially it is still called General Studies Paper-1 and Paper-2), intends to focus on analytical abilities and understanding rather than the ability to memorize. The new pattern includes two papers of two hours duration and 200 marks each.[10]  Both papers have multiple choice objective type questions only.[10] They are as under:

text:
Paper I tests the candidate's knowledge on current events, history of India and Indian national movement, Indian and world geography, Indian polity panchayti Raj system and governance, economic and social development, environmental ecology, biodiversity, climate change and general science, Art and culture.[10]
Paper II tests the candidates' skills in comprehension, interpersonal skills, communication, logical reasoning, analytical ability, decision making, problem solving, basic numeracy, data interpretation, English language comprehension skills and mental ability.[10]

text: In August 2014, the Centre announced that English marks in CSAT-II will not be included for gradation or merit and 2011 candidates may get a second chance to appear for the test next year.[11]

text: In May 2015, the Government of India announced that Paper II of the preliminary examination will be qualifying in nature i.e. it wouldn't be graded for eligibility in Mains Examination & a candidate needs to secure at least 33% marks in order to be eligible for graded on basis of marks of Paper I of Preliminary Examination.[1]

text: Mains[edit]

text: The Civil Services Mains Examination consists of a written examination and an interview.[1][12]

text: Examination[edit]

text: The written examination consists of nine papers, two qualifying and seven rankings  in nature. The range of questions may vary from just one mark to sixty marks, twenty words to 600 words answers. Candidates who pass qualifying papers are ranked according to marks and a selected number of candidates are called for interview or a personality test at the Commission's discretion.

text: According to the new marks allocations in Civil Service Examination 2013 there are some changes made in the examination according to the suggestion of the Prof. Arun. S. Nigavekar Committee.[13] However, after some controversy, the qualifying papers for Indian languages and English were restored to the examination.[14]

text:
Civil Services New Mains Format

Paper
Subject
Marks

Paper A
(One of the Indian languages listed below, to be selected by the candidate (from the languages listed in the Eighth Schedule to the Constitution of India) (Qualifying)
300

Paper B
English (Qualifying)
300

Paper I
Essay
250

Paper II
General Studies I (Indian heritage and culture, history and geography of the world and society)
250

Paper III
General Studies II (Governance, constitution, polity, social justice and international relations)
250

Paper IV
General Studies III (Technology, economic development, bio-diversity, environment, security and disaster management)
250

Paper V
General Studies IV(ethics, integrity and aptitude)
250

Papers VI, VII
Two papers on subjects to be selected by the candidate from the list of optional subjects below (250 marks for each paper)
500

Sub Total (Written Test)
1750

Personality Test (Interview)
275

Total Marks
2025

text: List of Languages[edit]

text: The examination is offered in the following languages, with the name of the script in braces:[15]

text:
Assamese (Assamese)
Bengali (Bengali)
Bodo (Devanagari)
Dogri (Devanagari)
English (English)
Gujarati (Gujarati)
Hindi (Devanagari)
Kannada (Kannada)
Kashmiri (Persian)
Konkani (Devanagari)
Maithili (Devanagari)
Malayalam (Malayalam)
Manipuri (Bengali)
Marathi (Devanagari)
Nepali (Devanagari)
Odia (Odia)
Punjabi (Gurumukhi)
Sanskrit (Devanagari)
Santhali (Devanagri or Ol Chiki)
Sindhi (Devanagari or Arabic)
Tamil. (Tamil)
Telugu (Telugu)
Urdu (Persian)

text: Optional subjects[edit]

text: The subjects available for Papers VI and VII are:[15] Public administration is one of the most sought after optional subjects in Mains examination as it has overlapping content with other subjects like Current Affairs, History, Polity. The standards of Optional papers is of honours level. Paper I is theoretical but Paper II is often dominated by Current Affairs and Application based questions.

text:
Agriculture
Animal Husbandary and Veterinary Science
Anthropology
Botany
Chemistry
Civil Engineering
Commerce and Accountancy
Economics
Electrical Engineering
Geography
Geology
History
Law
Literature of any one of the languages listed above
Management
Mathematics
Mechanical Engineering
Medical Science
Philosophy
Physics
Political Science and International Relations
Psychology
Public Administration
Sociology
Statistics
Zoology

text: Interview[edit]

text: Officially called the "Personality Test", the objective of the interview is to assess the personal suitability of the candidate for a career in public service by a board of competent and unbiased observers. The test is intended to evaluate the mental calibre of a candidate. In broad terms, this is really an assessment of not only a candidate's intellectual qualities, but also social traits and interest in current affairs. Some of the qualities to be judged are mental alertness, critical powers of assimilation, clear and logical exposition, balance of judgement, variety and depth of interest, ability for social cohesion and leadership, and intellectual and moral integrity.

text: The technique of the interview is not that of a strict cross-examination, but of a natural, though directed and purposive conversation that is intended to reveal the mental qualities of the candidate.

text:
The interview is not intended to be a test either of the specialised or general knowledge of the candidate, which has been already tested through written papers. Candidates are expected to have taken an intelligent interest not only in their special subjects of academic study, but also in the events which are happening around them both within and outside their own state or country as well as in modern currents of thought and in new discoveries which should rouse the curiosity of all well-educated youth.
The interview standards are very high and require thorough preparation as well as commitment.