Question

Calculate the coefficient of correlation for the ages of husbands and their respective wives:

Age of husbands	23	27	28	29	30	31	33	35	36	39
Age of wives	18	22	23	24	25	26	28	29	30	32

Answer 1

Without deviation:

Age of husbands (X)	Age of wives (Y)	X2	Y2	XY
23	18	529	324	414
27	22	729	484	594
28	23	784	529	644
29	24	841	576	696
30	25	900	625	750
31	26	961	676	806
33	28	1089	784	924
35	29	1225	841	1015
36	30	1296	900	1080
39	32	1521	1024	1248
311	257	9875	6763	8171

∑X = 311, ∑Y = 257, ∑X² = 9875, ∑Y² = 6763, ∑XY = 8171

N = 10

Coefficient of correlation

r = `("N"sum"XY" - (sum"X")(sum"Y"))/(sqrt("N"sum"X"^2 - (sum"X")^2) sqrt ("N"sum"Y"^2 - (sum"Y")^2))`

= `(10 xx 8171 - 311 xx 257)/(sqrt (10 xx 9875 - (311)^2) sqrt(10 xx 6763 - (257)^2))`

= `(81710 - 79927)/(sqrt (98750 - 96721) sqrt (67630 - 66049))`

= `1783/(45 xx 39.76)`

= 0.9965