Q.Find the mean deviation about the median for the following data: $3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21$.

The median is the middle value of an ordered dataset, so arranging the data in ascending or descending order is the first necessary step to compute it.

The median of a set of observations is the value that divides the data into two equal halves when arranged in order of magnitude. To locate this middle value (or …

With median 9, the average absolute deviation of the 9 values works out to $40/9$.

Sort the data: $3, 4, 5, 7, 9, 10, 12, 18, 19$ ($n=9$, odd).

Median = middle (5th) value $= 9$.

Absolute deviations $|x_i - 9|$: $6, 5, 4, 2, 0, 1, 3, 9, 10$

Sum of deviations $= 6+5+4+2+0+1+3+9+10 = 40$

…