1.

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. 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 = \(\frac{13+14}{2} = 13.5\)

xi101111121313141616171718
|xi-M|3.52.52.51.50.50.50.52.52.53.53.54.528

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 = \(\frac{46+49}{2} = 47.5\)

xi36424546464951536072
|xi-M|11.55.52.51.51.51.53.55.512.524.570

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


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