NCERT Solutions
Class 11 Maths
Statistics

Ex.15.1 Q.4
Find the mean deviation about the median for the data.
36, 72, 46, 42, 60, 45, 53, 46, 51, 49
The given data is
36, 72, 46, 42, 60, 45, 53, 46, 51, 49
Here, the numbers of observations are 10, which is even.
Arranging the data in ascending order, we obtain
36, 42, 45, 46, 46, 49, 51, 53, 60, 72
Median, M = [( )th observation + (
+ 1) th observation] ÷ 2
= [5th observation + 6th observation] ÷ 2
= (46 + 49) ÷ 2
= 95 ÷ 2 = 47.5
The deviations of the respective observations from the median, i.e., xi - M are
–11.5, –5.5, –2.5, –1.5, –1.5, 1.5, 3.5, 5.5, 12.5, 24.5
The absolute values of the deviations |xi - M| are
11.5, 5.5, 2.5, 1.5, 1.5, 1.5, 3.5, 5.5, 12.5, 24.5
The required mean deviation about the median is
MD(X) = (Σi=110|xi – M|) ÷ 10
= (11.5 + 5.5 + 2.5 + 1.5 + 1.5 + 1.5 + 3.5 + 5.5 + 12.5 + 24.5) ÷ 10
= 70 ÷ 10 = 7