Sum of the absolute deviations remains minimum with respect to - Vidyadip

MCQ

Sum of the absolute deviations remains minimum with respect to

A
mean
✓
median
C
mode
D
geometric mean

✓

Answer

Correct option: B.

median

b
Minimum deviation (MD) from mean $=\frac{\sum|X-\bar{X}|}{n}$

MD from median $=\frac{\sum \mid X-\text { median } \mid}{n}$

MD from mode $=\frac{\sum \mid X-\text { mode } \mid}{n}$

Since median $>$ mean $(\bar{X})$ and median $>$ mode.

So, It is clear that the mean deviation from median has the least value.

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