$\begin{array}{c|c} class& 1 - 3 & 4 - 6 & 7 - 9\\ \hline Frequency & 5 & 8 & 5\end{array}$
Find the standard deviation of the data using the table above

$\sqrt{6}$

$\frac{5}{3}$

$\sqrt{5}$

Correct answer is D

$\begin{array}{c|c} \text{class intervals} & Fre(F) & \text{class-marks(x)} & Fx & (x - x)& (x - x)^2 & F(x - x)^2 \\ \hline 1 - 3 & 5 & 2 & 10 & -3 & 9 & 45\\ 4 - 6 & 8 & 5 & 40 & 0 & 0 & 0 \\ 7 - 9 & 5 & 8 & 40 & 3 & 9 & 45 \\ \hline & 18 & & 90 & & & 90 \end{array}$

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

= $\frac{90}{18}$

= 5

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

= $\frac{90}{18}$

= $\sqrt{5}$

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Find the standard deviation of the data using the table above