Question:
Find the mean deviation about the mean for the data.
Solution:
$\mathrm{N}=\sum_{i=1}^{5} \mathrm{f}_{i}=25$
$\sum_{i=1}^{5} f_{i} x_{i}=350$
$\therefore \overline{\mathrm{X}}=\frac{1}{\mathrm{~N}} \sum_{\mathrm{i}=1}^{5} \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}=\frac{1}{25} \times 350=14$
$\therefore \mathrm{MD}(\overline{\mathrm{x}})=\frac{1}{\mathrm{~N}} \sum_{\mathrm{i}=1}^{3} \mathrm{f}_{\mathrm{i}}\left|\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}\right|=\frac{1}{25} \times 158=6.32$