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Question 142

The mean deviation about the median of the observations 3, 5, 6, 5, 8, 5, 4, 8, 7 and 9 is

Solution

Arrange the data in ascending order:
3,4,5,5,5,6,7,8,8,9
The median for this data = (5+6)/2 = 5.5

Now, mean deviation of data from median is given by: $$\Sigma\ \frac{\left|X-M\right|}{N}$$
where, X = Observation, M = Median, N = Number of observations

Summing up the deviations, we get: Numerator = 2.5+1.5+0.5+0.5+0.5+0.5+1.5+2.5+2.5+3.5 = 16
Number of observations = N = 10, hence, answer is 1.6

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