Question

Détermine the standared deviation for the following distribution.
Class Interval 11-13, 13-15 ,15-17, 17-19, 19 - 21, 21 - 23, 23 -25
frequency
3, 4, 5, 6 ,5, 4, 3​​

Answer 1

$Standard \: deviation \: = \sqrt{ \frac{ \sum \: f {x}^{2} }{n} \: - \: ( { \frac{ \sum \: fx}{n}) }^{2} }$

Applying this Formula :-

$\sigma \: = \: \sqrt{ \frac{384}{30} - ( { \frac{0}{30}) }^{2} }$

$\sigma \: = \sqrt{ \frac{384}{30} }$

$\sigma \: = \sqrt{12.4}$

${ \boxed{ \mathtt{ \sigma \: = \: 3.52}}}$

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Here we have used shortcut method this method is the same as used in case of discrete series as well. The only difference is that where as in discrete series deviation obtained of the actual values of the series in case of frequency distribution series deviations are obtained of the mid value of the class intervals.