The mean of absolute deviations of values of various observations from their median is called the mean deviation about the median.

Thus, if *x*1,*x*2,….*x*n be the n observations and M be their median then;

**n**

** Mean deviation = Σ | x****i**** – M |**

**i =1**

**n**

10.4.1 Methods of finding Mean deviation about Median:

**Case I: For discrete series:**

i) Let n1 be the number of those *x*i’^{s} for which *x*i ≥ M and let n2 be the number *x*i’^{s} for which *x*i < 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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