Find the variance and standard deviation for the following distribution: X:, 4.5, 14.5, 24.5, 34.5, 44.5, 54.5, 64.5 `f:` , 1, 5, 12, 22, 17, 9, 4

Answer

The standard deviation is `13.26`

Explanation

By using the formula for standard deviation:
$$
\begin{aligned}
&\mathrm{SD}=\sqrt{\operatorname{Var}(\mathrm{X})} \\
&\text { Mean }=\sum \frac{\mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}}{\mathrm{f}_{\mathrm{i}}} \\
&\text { So, } \\
&\text { Mean }=\frac{4.5+14.5+24+34.5+44.4+54.5+64.5}{7}=34.4
\end{aligned}
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