Question

What is the mean deviation about the mean for the following continuous frequency distribution?
$$\begin{array}{cc}\text{Value}& \text{Frequency}\\ 2-4& 5\\ 4-6& 6\\ 6-8& 3\\ 8-10& 1\end{array}$$

• A. 2.12
• B. 4.77
• C. 1.33
• D. 4.53

Answer 1

The correct option is C 1.33

$$\begin{array}{ccccc}\text{Value}& \text{Frequency}& x_i& f_i{x}_i& f_i|x_i-x|\\ 2-4& 5& 3& 15& 10\\ 4-6& 6& 5& 30& 0\\ 6-8& 3& 7& 21& 6\\ 8-10& 1& 9& 9& 4\\ \sum & 15& & 75& 20\end{array}$$

$\mathrm{Mean}\left(\overline{x}\right)=\frac{{\sum }^{}{f}_i{x}_i}{\sum _{}{f}_i}=\frac{75}{15}=5$
$\mathrm{Mean}\mathrm{deviation}\mathrm{about}\mathrm{the}\mathrm{mean}=\frac{{\sum }^{}{f}_i\left(x_i-\overline{x}\right|}{\sum _{}{f}_i}=\frac{20}{15}=1.33$