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 6th and 7th 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 5th and 6th 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 = \(\frac{\sum^n_{i=1}|x_i-M|}{n} = \frac{70}{10} =7.\)