Question

Measurements are made to the nearest cm. of the heights of 10 children. Calculate mean and standard deviation.

Heights (cms)	60	61	62	63	64	65	66	67	68
No. of children	2	0	15	29	25	12	10	4	3

Answer 1

Height (X)	Frequency (f)	fX	$\mathit{x}\mathbf{=}\left(\mathit{X}\mathbf{-}\overline{\mathit{X}}\right)$	x2	fx2
60	2	120	−3.89	15.13	30.26
61	0	0	−2.89	8.35	0
62	15	930	−1.89	3.57	53.55
63	29	1827	−0.89	0.79	22.91
64	25	1600	0.11	0.01	0.25
65	12	780	1.11	1.23	14.76
66	10	660	2.11	4.45	44.5
67	4	268	3.11	9.67	38.68
68	3	204	4.11	16.89	50.67
	Σf=100	ΣfX=6389			Σfx2=255.58

$$\begin{gathered} \mathrm{Mean},\overline{X}=\frac{\Sigma fX}{\Sigma f}=\frac{6389}{100}=63.89 \\ \mathrm{Standard}\mathrm{deviation},\left(\sigma \right)=\sqrt{\frac{\Sigma f{x}^2}{\Sigma f}}=\sqrt{\frac{255.58}{100}}=1.598=1.6\mathrm{cm}approx \end{gathered}$$
Hence mean of the above series is 63.89 cms and standard deviation is 1.6 cms.