Q.The mean deviation of the data is _______ when measured from the median.

The mean deviation of a data set about a point $A$ is $\dfrac{1}{n}\sum\lvert x_i-A\rvert$.

A standard result is that the sum of absolute deviations $\sum\lvert x_i-A\rvert$ is least when $A$ is the median of the data. Hence the mean deviation takes its smallest value when it is measured from the median (it is larger whe …

The property

For any data set, the mean deviation about a point $A$ is

As $A$ changes, this value changes. A standard result of statistics is that $\sum\lvert x_i-A\rvert$ attains its least value exactly when $A$ equals the median of the data.

Why the median minimizes it …