Descriptive Statistics Slides

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1 ( ) , squash, badminton . < 30 30-50 > 50 7 1 9 10 4 0 20 11 4 5 10 27 4 1 18 33

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2 . .i 1 0 - 2.5 2 2.5 - 5.0 3 5.0 - 7.5 4 7.5 - 10 5 10 fi 201 372 260 80 10 Fi 201 573 833 913 923 F i /n 0.218 0.621 0.902 0.989 1.000

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1. (Pies) 2. 3.

A B

fi 19 16

f i /n 0.543 0.457

A B

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1. (Pies) 2. 3. fi 19 16 f i /n 0.543 0.4570.560 0.540 0.520 0.500 0.480 0.460 0.440 0.420 0.400 A B

A B

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1. (Pies) 2. 3. 0-9 110 - 19 20 - 29 30 - 39 40 - 49 50 - 59 fi 5 11 20 9 13 7 f i /n% 7.7% 16.9% 30.8% 13.8% 20.0% 10.8%25

20

15

10

5

0 0 -- 9 10 -- 19 20 -- 29 30 -- 39 40 -- 49 50 -- 59

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1. (Pies) 2. 3. ( ) 0-9 110 - 19 20 - 29 30 - 39 40 - 49 50 - 59 fi 5 11 20 9 13 7 f i /n% 7.7% 16.9% 30.8% 13.8% 20.0% 10.8%25 20 15 10 5 0 0 -- 9 10 -- 19 20 -- 29 30 -- 39 40 -- 49 50 -- 59

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1. (Pies) 2. 3. () 0-9 110 - 19 20 - 29 30 - 39 40 - 49 50 - 59 fi 5 11 20 9 13 7 f i /n% 7.7% 16.9% 30.8% 13.8% 20.0% 10.8%25 20 15 10 5 0 0 -- 9

10 -- 19

20 -- 29

30 -- 39

40 -- 49

50 -- 59

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- - 0.4 0.3 0.2

0.1

1 2

-2

-1

0.12 0.1 0.08 0.06 0.04 0.02 2 4 6 8 10 12 14

x

( < m < x )x

0.8

0.6

0.4

0.2

( > m > x )0.2 0.4 0.6 0.8 1 1.2

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(Percentiles) , 100 p% 100 (1-p)% .

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(Percentiles)1. 2. 3. 4. (quartile) Q1 75% Q3 25% (Q2) k (n + 1) (Dk) 10

n +1 4

3( n + 1) 4

5. (Pk)

k (n + 1) 100

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(Percentiles) 1 4, 6, 7, 15, 18, 20, 25 n= 7, 7 +1 Q1 = 6 =2 4 3(7 + 1) = 6 Q3 = 20 4

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(Percentiles) 2 n= 8, 4, 6, 7, 15, 18, 20, 23, 25 Q1 = 6.25( 2 25% 3 .)

8 +1 = 2.25 4

3(8 + 1) = 6.75 4

Q3 = 22.25 ( 6

75% 7 .)

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q qn , , Fi-1 < q n Fi i- :

hi P = ai 1 + ( qn Fi 1 ) fi... " "

0-5 15 - 10 110 - 20 20 - 35 35 - 60 60 -100 fi 3 7 16 18 12 4 f i /h i 0,6 1,4 1,6 1,2 0,8 0,1 Fi 3 10 26 44 56 60

, Q3 , d7 , P5 .

Q2 = m , q = Q2 = 20 +15 18

1 2

, qn=

1 2

60 = 30

(30 - 26) = 23.33

hi P = ai 1 + ( qn Fi 1 ) fi... " "

0-5 15 - 10 110 - 20 20 - 35 35 - 60 60 -100 fi 3 7 16 18 12 4 f i /h i 0,6 1,4 1,6 1,2 0,8 0,1 Fi 3 10 26 44 56 60

, Q3 , d7 , P5 .

q=

3 4

, qn=25 12

3 4

60 = 45

Q3 = 35 +

(45 - 44) = 37.08

hi P = ai 1 + ( qn Fi 1 ) fi... " "

0-5 15 - 10 110 - 20 20 - 35 35 - 60 60 -100 fi 3 7 16 18 12 4 f i /h i 0,6 1,4 1,6 1,2 0,8 0,1 Fi 3 10 26 44 56 60

, Q3 , d7 , P5 .

q=

7 10

, qn=15 18

7 10

60 = 42

d7 = 20 +

(42 - 26) = 33.3

hi P = ai 1 + ( qn Fi 1 ) fi... " "

0-5 15 - 10 110 - 20 20 - 35 35 - 60 60 -100 fi 3 7 16 18 12 4 f i /h i 0,6 1,4 1,6 1,2 0,8 0,15 100

Fi 3 10 26 44 56 60

, Q3 , d7 , P5 .

q=

5 100

, qn=5 3

60 = 3

P5 = 0 +

(3 - 0) = 5

hi P = ai 1 + ( qn Fi 1 ) fi... " "

(skewness) 1 n ( xi x )3 ' m3 n i =1 g1 = = 3 3 ' 2 n (m2 ) 1 ( x x )2 2 i n i =1

0.12

0.1 0.08 0.06 0.04 0.02 2 4 6 8 10 12 14

g1> 0

0.8

0.6

x

0.4

g1< 0 1 1.2

0.2

0.2

0.4

0.6

0.8

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(Kurtosis)g2 =0.4

(m )

' m4

' 2 2

3=

1 n ( xi x )4 n i =1 1 ( xi x )2 n i =1 n 2

3

0.3

0.2

0.1

g2 . (outliers)2 4

-4

-2

0.4

0.3

0.2

0.1

g2 .2 4

-4

-2

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Box Plots-100 2 4 6 8 12 15 13 25 23 36 35 38 34 29 9 10 30 27 100 42 38 53 -23 -33 -15 -16 -17 -9 -4 -5 5 -11 -3 -2 95 92 -60 33 -33Statistics var Mean Median Variance Skewness Kurtosis Minimum Maximum Percentiles 25 50 75 12.08 9.50 1,428.328 -0.080 1.898 -100 100 -8.00 9.50 33.75

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Box Plots-100 2 4 6 8 12 15 13 25 23 36 35 38 34 29 9 10 30 27 100 42 38 53 -23 -33 -15 -16 -17 -9 -4 -5 5 -11 -3 -2 95 92 -60 33 -33100A A

50

var

0

-50

-100

A

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