Find the mean deviation about the median for the data 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

Solution:

The given data is 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

Here,

the numbers of observations are 12 , i.e., even.

Arranging the above data in ascending order,

we obtain 10, 11, 11, 12, 13, 13, 14, 16, 16, 17, 17, 18

Median of the data

M = [(12/2)^th observation + (12/2 + 1)^th observation]/2

= [6^th observation + 7^th observation]/2

= (13 + 14)/2

= 27/2

= 13.5

The deviations of the respective observations from the median, i.e., x_i - 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, |x_i - 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

M.D. (x) = ¹²∑_{i = 1} (|x_i - x|)/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

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NCERT Solutions Class 11 Maths Chapter 15 Exercise 15.1 Question 3

Find the mean deviation about the median for the data 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

Summary:

The mean deviation about the median for the given data is 2.33