Find the mean deviation about the mean for the data
Height in cms 95-105 105-115 115-125 125-135 135-145 145-155
Number of boys  9           13         26           30          12           10

Solution:

The following table is formed.

Height in cms	Number of boys fi	Mid-point xi	fixi	xi - x	fixi - x
95 -105	9	100	900	25.3	227.7
105 -115	13	110	1430	15.3	198.9
115 -125	26	120	3120	5.3	137.8
125 -135	30	130	3900	4.7	141
135 -145	12	140	1680	14.7	176.4
145 -155	10	150	1500	24.7	247
Total	100		12530		1128.8

Here,

N = ⁶∑_{i = 1} f_i = 100 and ⁶∑_{i = 1} f_i|x_i - M| = 12530

Therefore,

x = 1/N ⁶∑_{i = 1} f_ix_i

= 1/100 × 12530

= 125.3

Hence, the mean deviation about the median

M.D. (x) = ⁶∑_{i = 1} |x_i - x|

= 1/100 × 1128.8

= 11.28

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NCERT Solutions Class 11 Maths Chapter 15 Exercise 15.1 Question 10

Find the mean deviation about the mean for the data  Height in cms 95-105 105-115 115-125 125-135 135-145 145-155 Number of boys  9           13         26           30          12           10

Summary:

The mean deviation about the mean for the given data is 11.28