Question

What is the mean deviation about mean for the following discrete frequency distribution?
$$\begin{array}{cc}\text{Value}& \text{Frequency}\\ 1& 1\\ 10& 2\\ 15& 1\\ 20& 2\\ 30& 2\end{array}$$

• A. 7.1
• B. 8
• C. 9.34
• D. 13

Answer 1

The correct option is B 8

$$\begin{array}{cccc}\text{Value}& \text{Frequency}& f_i{x}_i& f_i|x_i-x|\\ 1& 1& 1& 16\\ 10& 2& 20& 14\\ 15& 1& 15& 2\\ 20& 2& 40& 6\\ 30& 2& 60& 26\\ \sum & 8& 136& 64\end{array}$$
$\mathrm{The}\mathrm{mean}\overline{x}=\frac{{\sum }^{}{f}_i{x}_i}{{\sum }^{}{f}_i}=\frac{136}{8}=17$
Mean deviation (Mean) = $\frac{{\sum }^{}{f}_i\left(x_i-\overline{x}\right|}{{\sum }^{}{f}_i}=\frac{64}{8}=8$