Find the mean deviation about the mean for the data

Question:

Find the mean deviation about the mean for the data

Solution:

The following table is formed.

Here, $N=\sum_{i=1}^{6} f_{i}=100, \sum_{i=1}^{6} f_{i} x_{i}=12530$

$\therefore \overline{\mathrm{x}}=\frac{1}{\mathrm{~N}} \sum_{\mathrm{i}=1}^{6} \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}=\frac{1}{100} \times 12530=125.3$

M.D. $(\bar{x})=\frac{1}{N} \sum_{i=1}^{6} f_{i}\left|x_{i}-\bar{x}\right|=\frac{1}{100} \times 1128.8=11.28$

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