$\begin{array}{c|c} Class Interval & 3 - 5 & 6 - 8 & 9 - 11 \\ \hline Frequency & 2 & 2 & 2 \end{array}$ . Find the standard deviation of the above distribution.

√5

√6

√7

√2

Correct answer is B

$\begin{array}{c|c}Class Interval & 3 - 3 & 6 - 8 & 9 - 11 \\ x & 4 & 7 & 10 \\ f & 2 & 2 & 2 \\ f - x & 8 & 14 & 20 \\ |x - \bar{x}|^2 & 9 & 0 & 9 \\ |x - \bar{x}|^2 & 18 0 & 18 \end{array}$

$\bar{x}$ = $\frac {\sum fx}{\sum f}$

= $\frac {8 + 14 + 20}{2 + 2 + 2}$

= $\frac{42}{6}$

$\bar{x}$ = 7

S.D = $\sqrt\frac{\sum f(x - \bar{x})^2}{\sum f}$

= $\sqrt\frac{18 + 0 + 18}{6}$

= $\sqrt\frac{36}{6}$

= $\sqrt {6}$

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