Find the mean deviation about the median for the data.

Let us make the table of the given data and append other columns after calculations.

Now, N = 26, which is even.

Median is the mean of the 13^th and 14^th observations. Both of these observations lie in the cumulative frequency 14, for which the corresponding observation is 7.

Then,

Median = \( \dfrac{ (13^{th} observation + 14^{th} observation)}{2}\)

= \( \dfrac{ (7 + 7)}{2}\)

= \( \dfrac{14}{2}\)

= 7

So, the absolute values of the respective deviations from the median, i.e., |x_i – M| are shown in the table.

Therefore,

\( \displaystyle\sum_{i=1}^{6} f_i =26\) and \(\)\( \displaystyle\sum_{i=1}^{8} f_i|X_i-M|=84\)

\( \overline{X} = \dfrac{1}{N} \displaystyle\sum_{i=1}^{6} f_i |X_i-M|\)

= \( \dfrac{1}{26}\times 84\)

= 3.23