Question

Find the mean deviation about the median for the data

xi	15	21	27	30	35
fi	3	5	6	7	8

Answer 1

The given observations are already in ascending order.

Adding a column corresponding to cumulative frequencies of the given data, we obtain the following table.

$x_i$	$f_i$	$c.f$
15	3	3
21	5	8
27	6	14
30	7	21
35	8	29

Here, N = 29, which is odd.

∴ Median= $(\frac{29+1}{2})^{th}$ observation = 15th observation.

This observation lies in the cumulative frequency 21, for which the corresponding observation is 30.

∴ Median = 30

The absolute values of the deviations from median, i.e $|x_i-M|,$ are

$|x_i,M|$| 15| 9| 3| 0| 5
---|---|---|---|---|---
$f_i$| 3| 5| 6| 7| 8
$f_i|x-M|$| 45| 45| 18| 0| 40

$\sum_{I=1}^{5}f_i=29$ , $\sum_{I=1}^{5}f_i|x_i-M|=148$

$=M.D.(M)=\frac{1}{N}\sum_{i=1}^{5}f_i|x_i-M|=\frac{1}{29}×148=5.1$