![\[\begin{tabular}{|l|l|l|l|l|l|} \hline \text { Class interval } & 0-4 & 4-8 & 8-12 & 12-16 & 16-20 \\ \hline \text { Frequency } & 4 & 6 & 8 & 5 & 2 \\ \hline \end{tabular}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-89e2ff7ca4a076d66a84b3171bda25fa_l3.png "Rendered by QuickLaTeX.com")
Solution:
The frequency distribution is given
We now need to find the mean deviation about the mean
Let’s construct a table of the given data and append other columns after calculations
![\[\begin{tabular}{|l|l|l|l|} \hline Class interval & Mid - Value $\left(x_{i}\right)$ & Frequency $\left(f_{i}\right)$ & $f_{i} x_{i}$ \\ \hline $0-4$ & 2 & 4 & 8 \\ \hline $4-8$ & 6 & 6 & 36 \\ \hline $8-12$ & 10 & 8 & 80 \\ \hline $12-16$ & 14 & 5 & 70 \\ \hline $16-20$ & 18 & 2 & 36 \\ \hline & total & 25 & 230 \\ \hline \\ \end{tabular}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9f2dba3a3731f5639901bfed26f29bcb_l3.png "Rendered by QuickLaTeX.com")
Mean here, 
We need to find the mean deviation
![\[\begin{tabular}{|l|l|l|l|l|l|} \hline Class interval & Mid -Value $\left(\mathrm{x}_{\mathrm{i}}\right)$ & Frequency $\left(\mathrm{f}_{\mathrm{i}}\right)$ & $\mathrm{f}_{\mathrm{i}} \mathrm{X}_{\mathrm{i}}$ & $\mathrm{d}_{\mathrm{i}}=\mid \mathrm{x}_{\mathrm{i}}-$ mean $\mid$ & $\mathrm{f}_{\mathrm{i}} \mathrm{d}_{\mathrm{i}}$ \\ \hline $0-4$ & 2 & 4 & 8 & $7.2$ & \\ \hline $4-8$ & 6 & 6 & 36 & $3.2$ & $28.8$ \\ \hline $8-12$ & 10 & 8 & 80 & $0.8$ & $19.2$ \\ \hline $12-16$ & 14 & 5 & 70 & $1.8$ & $6.4$ \\ \hline $16-20$ & 18 & 2 & 36 & $8.8$ & $24.4$ \\ \hline & total & 25 & 230 & & $17.6$ \\ \hline \end{tabular}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c3b2ad381cb3125af3ff90152eda1a57_l3.png "Rendered by QuickLaTeX.com")
As a result, Mean Deviation becomes,
As a result, 
is the mean deviation about the mean of the distribution.