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 :- Table for calculating Karl Pearson’s coefficient of correlation.

n=10

suppose ,we select the mean of x= 14 and the mean of y= 310

Price Demand u= x-14 v=(y-310)/10 u.v u^2 v^2

(x) (y)

10 420 -4 11 -44 16 121

11 410 -3 10 -30 9 100

12 400 -2 9 -18 4 81

13 310 -1 0 0 1 0

14 280 0 -3 0 0 9

15 260 1 -5 -5 1 25

16 240 2 -7 -14 4 49

17 210 3 -10 -30 9 100

18 210 4 -10 -40 16 100

19 200 5 -11 -55 25 121

=5 -16 -236 85 706

coefficient of correlation (r)

coefficient of correlation (r) = [n( Σu.v)-{( Σu)( Σv)}] / [√{n( Σ u^2)-( Σ u)^2} *√{n( Σ v^2)-( Σ v)^2 }]

= {10*(-236)+ 5*16} /{ √(10*85 - 25)* √(10*706 - 256)}

= -0.9623

Hence , the Karl Pearson’s coefficient of correlation is -0.9623. (Ans)