Question

calculate karl pearson coefficient of correlation between price and quantity demanded of a commodity ​

Answer 1

Let price be X and quantity be Y

X: X Values

Y: Y Values

Mx: Mean of X Values

My: Mean of Y Values

X - Mx & Y - My: Deviation scores

(X - Mx)2 & (Y - My)2: Deviation Squared

(X - Mx)(Y - My): Product of Deviation Scores

X Values

∑ = 55

Mean = 11

∑(X - Mx)2 = SSx = 4

Y Values

∑ = 20

Mean = 4

∑(Y - My)2 = SSy = 10

X and Y Combined

N = 5

∑(X - Mx)(Y - My) = -6

Calculating Karl pearson's coefficient r,

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -6 / √((4)(10)) = -0.9487

The value of R is -0.9487.

This is a strong negative correlation, which means that high price go with low quantity (and vice versa).