Question

Find the mean deviation about the median for the following data:

1. 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17.

2. 36, 72, 46, 42, 60, 45, 53, 46, 51, 49.

Answer 1

1. Arrange the data in the ascending order we have;

10, 11, 11, 12, 13, 13, 14, 16, 16, 17, 17, 18

Here n = 12. So median is the average of 6^th and 7^th observations.

Therefore; Median, M = \(\frac{13+14}{2} = 13.5\)

xi	10	11	11	12	13	13	14	16	16	17	17	18
|xi-M|	3.5	2.5	2.5	1.5	0.5	0.5	0.5	2.5	2.5	3.5	3.5	4.5	28

Mean deviation = \(\frac{\sum^n_{i=1}|x_i-M|}{n} = \frac{28}{12} = 2.33\)

2. Arrange the data in the ascending order we have; 36, 42, 45, 46, 46, 49, 51, 53, 60, 72

Here n = 10. So median is the average of 5^th and 6^th observations.

Therefore; Median, M = \(\frac{46+49}{2} = 47.5\)

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

Mean deviation =  \(\frac{\sum^n_{i=1}|x_i-M|}{n} = \frac{70}{10} =7.\)