The mean of absolute deviations of values of various observations from their median is called the mean deviation about the median.
Thus, if x1,x2,….xn be the n observations and M be their median then;
Mean deviation = Σ | xi – M |
10.4.1 Methods of finding Mean deviation about Median:
Case I: For discrete series:
i) Let n1 be the number of those xi’s for which xi ≥ M and let n2 be the number xi’s for which xi < M. then n1 +n2 = n.
ii) Let s1 and s2 denote the sum of n1 and n2 observations respectively. Then,
Mean deviation = (s1 – s2) – (n1 – n2)M/ (n1 + n2)
Case II: For Grouped Data:
i) Let n1 be the sum of frequencies fi’s of those xi’s for which xi < M and let s1 = Σ fi xi for these fi’s.
ii) Let n2 be the sum of frequencies fi’s of those xi’s for which xi < M and let s2 = Σ fi xi for these fi’s.
Mean Deviation = (s1 – s2) – (n1 – n2)M/ (n1 + n2)
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