Consider the following grouped frequency distribution :Class 0-10 10-20 20-30 30-40 40-50 50-60 Frequency 1 2 4 6 4 3
What is the mean deviation about the mean ?
10.65
Using class midpoints \(5,15,25,35,45,55\) and frequencies \(1,2,4,6,4,3\), \(N=20,\ \sum f_ix_i=690\) and \(\bar{x}=34.5\).
The weighted absolute deviations are \(29.5,39,38,3,42,61.5\), totalling \(213\). Hence the midpoint-based mean deviation about the mean is \(\frac{\sum f_i|x_i-34.5|}{20}=\frac{213}{20}=10.65\).
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