Question

Find the standard deviation for the following data:

x :	3	8	13	18	23
f :	7	10	15	10	6

Answer 1

\[x_i\]	\[f_i\]	\[f_i x_i\]	\[\left( x_i - \bar{X} \right)\]	\[\left( x_i - \bar{X} \right)^2\]	\[f_i \left( x_i - \bar{X} \right)^2\]
3	7	21	−9.79	95.84	670.88
8	10	80	−4.79	22.94	229.4
13	15	195	0.21	0.04	0.6
18	10	180	5.21	27.14	271.4
23	6	138	10.21	104.24	625.44
	\[\sum f_i = 48\]	\[\sum f_i x_i = 614\]			\[\sum f_i \left( x_i - \bar{X} \right)^2 = 1797 . 32\]

Variance,

\[\sigma^2 = \frac{\sum f_i \left( x_i - \bar{X} \right)^2}{\sum f_i} = \frac{1797 . 32}{48} = 37 . 44\]

\[SD, \sigma = \sqrt{37 . 44} = 6 . 12\]