Question

Find Karl Pearson’s correlation coefficient between density of population (per square km) and death rate (per thousand) from the following data:

City	A	B	C	D	E	F	G
density (per sq km)	750	600	350	500	200	700	850
Death rate (per thousand)	30	20	15	20	10	25	50

Answer 1

Here, n = 7: x = Density, y = Death rate.

We calculate the correlation coefficient by shortcut method obtaining new variables u and v and the table for calculation is prepared as follows:

Karl Pearson’s correlation coefficient:

Now, \(r = \frac{nΣuv−(Σu)(Σv)}{\sqrt{nΣu^2−(Σu)^2}⋅\sqrt{nΣv^2−(Σv)^2}}\)

Putting n = 7, Σuv = 71, Σu = 9, Σv = 6, Σu² = 139 and Σv² = 46 in the formula,

Hence, Karl Pearson’s correlation coefficient between density of population and death rate obtained is 0.88.