Question

1. Find the mean and the Variance of the following sample data:

           

x	Frequency (f)
1	5
2	6
4	9
8	6
12	4

Answer 1

x	Frequency (f)	Relative frequency	x^2	x(px)	x^2(pX)
1	5	0.1667	1	0.166666667	0.166666667
2	6	0.2	4	0.4	0.8
4	9	0.3	16	1.2	4.8
8	6	0.2	64	1.6	12.8
12	4	0.1333	144	1.6	19.2
					sum= 37.7667
				Mean= 4.9667

Variance =

V(x) = E(x^2) - E(x)^2 =

37.7667 - 24.6681 = 13.0986