Question

The lengths (in cm) of 10 rods in a shop are given below:
40.0, 52.3, 55.2, 72.9, 52.8, 79.0, 32.5, 15.2, 27.9, 30.2
 Find mean deviation from median

Answer 1

 Formula for the mean deviation from the median is as follows:

\[MD = \frac{1}{n} \sum^n_{i = 1} \left| d_i \right|, \text{ where } \left| d_i \right| = \left| x_i - M \right|\]

Arranging the data in ascending order for finding the median:
15.2, 27.9, 30.2, 32.5, 40, 52.3, 52.8, 55.2, 72.9, 79

Here, 

n = 10. 

Therefore, median is the average of the fifth and the sixth observations.

\[M = \frac{40 + 52 . 3}{2} = 46 . 15\]

\[x_i\]	\[\left| d_i \right| = \left| x_i - 46 . 15 \right|\]
40	6.15
52.3	6.15
55.2	9.05
72.9	26.75
52.8	6.65
79	32.85
32.5	13.65
15.2	30.95
27.9	18.25
30.2	15.95
Total	166.4

\[MD = \frac{1}{10} \times 166.4 = 16.64\]

Mean deviation from median in 16.64cm.