Math Assignment Help With Mean Deviation About The Median

10.4 Mean Deviation about the Median: 

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;

n

Mean deviation = Σ | xi – 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 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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