Question

What is the variance of the following data ?
$$\begin{array}{cc}\text{Value}& \text{Frequency}\\ 4& 1\\ 2& 2\\ 0& 2\\ -2& 2\\ -4& 1\end{array}$$

• A. 6
• B. 3
• C. 5
• D. 0.0

Answer 1

The correct option is A 6

$$\begin{array}{cccc}\text{Value}& \text{Frequency}& f_i{x}_i& f_i(x_i-\overline{x}{)}^2\\ 4& 1& 4& 16\\ 2& 2& 4& 8\\ 0& 2& 0& 0\\ -2& 2& -4& 8\\ -4& 1& -4& 16\\ \sum & 8& 0& 48\end{array}$$
$\mathrm{Mean}x=\frac{{\sum }^{}{f}_i{x}_i}{\sum _{}{f}_i}=0$
$\mathrm{Variance}=\frac{{\underset{}{\overset{}{\sum f_i{\left(x_i-x\right)}^2}}}^{}}{\sum _{}{f}_i}=\frac{48}{8}=6$