NCERT Solutions
Class 11 Maths
Statistics

Ex.15.1 Q.3
Find the mean deviation about the median for the data.
13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17
The given data is
13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17
Here, the numbers of observations are 12, which is even.
Arranging the data in ascending order, we obtain
10, 11, 11, 12, 13, 13, 14, 16, 16, 17, 17, 18
Median, M = [( ) th observation + (
+ 1) th observation] ÷ 2
= [6th observation + 7th observation] ÷ 2
= (13 + 14) ÷ 2
= 27 ÷ 2 = 13.5
The deviations of the respective observations from the median, i.e., xi - M are
–3.5, –2.5, –2.5, –1.5, –0.5, –0.5, 0.5, 2.5, 2.5, 3.5, 3.5, 4.5
The absolute values of the deviations |xi - M| are
3.5, 2.5, 2.5, 1.5, 0.5, 0.5, 0.5, 2.5, 2.5, 3.5, 3.5, 4.5
The required mean deviation about the median is
MD(X) = (Σi=112|xi – M|) ÷ 12
= (3.5 + 2.5 + 2.5 + 1.5 + 0.5 + 0.5 + 0.5 + 2.5 + 2.5 + 3.5 + 3.5 + 4.5) ÷ 12
= 28 ÷ 12
= 2.33