Question

The sum of absolute deviation is least when taken from

• A. Mean
• B. Median
• C. Mode
• D. None of the above

Answer 1

The correct option is B

Median

Explanation for the correct answer:

Option(B):Median

Minimum deviation (MD) from mean $=\frac{\sum |\mathrm{X}-\overline{\mathrm{X}}|}{\mathrm{n}}$
MD from median $=\frac{\sum \mid \mathrm{X}-\text{median}\mid }{\mathrm{n}}$
MD from mode $=\frac{\sum \mid \mathrm{X}-\text{mode}\mid }{\mathrm{n}}$
Since median $>$ mean $\left(\overline{\mathrm{X}}\right)$ and median $>$ mode.

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

Hence, option(B)Median is the correct answer.

Explanation for the incorrect answer:

Option(A),Option(C) and Option(D):

The sum of absolute deviations is minimum when taken around the median.

So, options(A),(C) and (D) are incorrect answers.

Therefore, option(B) is the correct answer.