x12345f21212 x 1 2 3 4 5 f 2 1 2 1 2 Find the variance of the frequency distribution above

Question 1 Report

$\begin{array}{cc} x & 1 & 2 & 3 & 4 & 5 \\ f & 2 & 1 & 2 & 1 & 2 \end{array}$

Find the variance of the frequency distribution above

\frac{3}{2}

\frac{9}{4}

\frac{5}{2}

3

Answer Details

$\begin{matrix} x & f & f x & \bar{x} ? x & (\bar{x} ? x)^{2} & f (\bar{x} ? x)^{2} \\ 1 & 2 & 2 & ? 2 & 4 & 8 \\ 2 & 1 & 2 & ? 1 & 1 & 1 \\ 3 & 2 & 6 & 0 & 0 & 0 \\ 4 & 1 & 4 & 1 & 1 & 1 \\ 2 & 2 & 10 & 2 & 4 & 8 \\ 8 & 24 & 18 \end{matrix}$
x = $\frac{\sum f x}{\sum f}$
= $\frac{24}{8}$
= 3
Variance (62) = $\frac{\sum f (\bar{x} - x)^{2}}{\sum f}$
= $\frac{18}{8}$
= $\frac{9}{4}$

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