Question

Find the mean deviation about the median for the data.

36, 72, 46, 42, 60, 45, 53, 46, 51, 49

Answer 1

Writing the given data in ascending order

36, 42, 45, 46, 46, 49, 51, 53, 60, 72

n = 10

∴ ${\displaystyle \frac{10}{2}}$ = 5th term = 46, and 5 + 1 = 6th term = 49

∴ Median = ${\displaystyle \frac{46+49}{2}}$

= ${\displaystyle \frac{95}{2}}$

= 47.5

xi	|xi - 47.5|
36	11.5
42	5.5
45	2.5
46	1.5
46	1.5
49	1.5
51	3.5
53	5.5
60	12.5
72	24.5
Total	70

Mean deviation (M) = ${\displaystyle \frac{\sum |x_i-\text{M}|}{n}}$

= ${\displaystyle \frac{70}{70}}$

= 7