From the following data relating to playing habits in various age groups of 900 students Calculate coefficient of correlation - Economics - Correlation

Question

From the following data relating to playing habits in various
age groups of 900 students Calculate coefficient of correlation
between age group and playing habits
Age group = 15-16, 16-17, 17-18, 18-19, 19-20, 20-21
No of students = 250, 200, 150, 120, 100, 80
Regular Players = 200, 150, 90, 48, 30, 12

Amit Chatterjee · Accepted Answer

X	Y	$x = X - \bar{X} x = X - 150$	$y = Y - \bar{Y} y = Y - 88.33$	x²	y²	xy
250	200	100	116.67	10000	13611.89	11667
200	150	50	66.67	2500	4444.889	3333.5
150	90	0	6.67	0	44.4889	0
120	48	-30	-35.33	900	1248.209	1059.9
100	30	-50	-53.33	2500	2844.089	2666.5
80	12	-70	-71.33	4900	5087.969	4993.1

900	530			$ x^{2} = 20800$	$ y^{2} = 27281.53$	$ x y = 23720$

$\bar{X} = \frac{Σ X}{n} = \frac{900}{6} = 150$

$\bar{Y} = \frac{Σ Y}{n} = \frac{530}{6} = 88.33$

$r = \frac{Σ x y}{\sqrt{Σ x^{2} \times Σ y^{2}}} = \frac{23720}{\sqrt{20800 \times 27281.53}} = 0.995$

Therefore, the correlation coefficient between the age group and playing habits is very high as it is closed to 1.