Question

Calculate Mean and Variance for the following frequency distribution:

X	:	1	2	3	4	5	6	7	8	9	10
f	:	2	5	8	16	21	18	13	10	4	3

Answer 1

X	f	fX	Deviation $$\begin{gathered} x=X\mathit{-}\overline{\mathit{X}} \\ \overline{\mathit{X}}=5.5 \end{gathered}$$	x2	fx2
1 2 3 4 5 6 7 8 9 10	2 5 8 16 21 18 13 10 4 3	2 10 24 64 105 108 91 80 36 30	−4.5 −3.5 −2.5 −1.5 −.5 .5 1.5 2.5 3.5 4.5	20.25 12.25 6.25 2.25 .25 .25 2.25 6.25 12.25 20.25	40.5 61.25 50 36 5.25 4.5 29.25 62.5 49 60.75
	Σf = 100	ΣfX = 550			Σfx2 = 399

$$\begin{gathered} \overline{\mathit{X}}=\frac{\mathrm{\Sigma }fX}{\mathrm{\Sigma }f}=\frac{550}{100}=5.5 \\ \mathrm{Variance}\left({\sigma }^2\right)=\frac{\mathrm{\Sigma }f{x}^2}{\mathrm{\Sigma }f}=\frac{399}{100}=3.99 \end{gathered}$$
Thus, mean and variance are 5.5 and 3.99 respectively.