Question

Calculate the Karl Pearson’s coefficient of correlation from the following pairs of

values and interpret the result:

Price (in Rs.) 10 11 12 13 14 15 16 17 18 19

Demand (in kgs) 420 410 400 310 280 260 240 210 210 200​

Answer 1

Given:

Price (in Rs.) 10 11 12 13 14 15 16 17 18 19

Demand (in kgs) 420 410 400 310 280 260 240 210 210 200​

To find:

Calculate the Karl Pearson’s coefficient of correlation from the following pairs of values and interpret the result:

Solution:

The table for calculation of r is given as follows:

Price (X)

10

11

12

13

14

15

16

17

18

19

Demand (Y)

420

410

400

310

280

260

240

210

210

200

u = X - 14

-4

-3

-2

-1

0

1

2

3

4

5

Total = 5

v = (Y-310)/10

11

10

9

0

-3

-5

-7

-10

-10

-11

Total = -16

uv

-44

-30

-18

0

0

-5

-14

-30

-40

-55

Total = -236

u^2

16

9

4

1

0

1

4

9

16

25

Total =85

v^2

121

100

81

0

9

25

49

100

100

121

Total 706

r = -10×236+5×16 / [√10×85-25 √10×706-256] = -0.96

Therefore, Karl Pearson’s coefficient of correlation is - 0.96