Question

Mean deviation is least when calculated from the median

Answer 1

Mean deviation is not related to median in any way.

Mean deviation is the mean of all the deviations of data.

A deviation is the difference between the mean of data and the data itself.

For exp: if we have 4 numbers : 2, 7 ,11, 4, 6

There mean would be : 6

And the mean deviations would be: 6-2 , 6-7, 6-11, 6-4, 6-6 or 4,-1,-5,2,0 respectively.

Taking the absolute values : 4,1,5,2, 0

The mean deviation would be (4+1+5+2+0) /5  = 2.4

Arranging the given data set into ascending order: 2,4,6,7,11

The median would be middle most element i.e. 6

Hence, the concept of median and mean deviations is totally different