Find the mean deviation about the mean for the data
Income per day (₹) Number of Persons
0-100                                    4
100-200                                8
200-300                                9
300-400                               10
400-500                                7
500-600                                5
600-700                                4
700-800                                3

Solution:

The following table is formed.

Income per day	Number of person fi	Mid-point xi	fi xi	xi - x	fi xi - x
0 -100	4	50	200	308	1232
100 - 200	8	150	1200	208	1664
200 - 300	9	250	2250	108	972
300 - 400	10	350	3500	8	80
400 - 500	7	450	3150	92	644
500 - 600	5	550	2750	192	960
600 - 700	4	650	2600	292	1168
700 - 800	3	750	2250	392	1176
Total	50		17900		7896

Here,

N = ⁸∑_{i = 1} f_i = 50 and ⁸∑_{i = 1} f_i|x_i - M| = 17900

Therefore,

x = 1/N ⁸∑_{i = 1} f_ix_i

= 1/50 × 17900

= 358

Hence, the mean deviation about the median

M.D. (x)

= ⁸∑_{i = 1} |x_i - x|

= 1/50 × 7896

= 157.92

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NCERT Solutions Class 11 Maths Chapter 15 Exercise 15.1 Question 9

Find the mean deviation about the mean for the data: Income per day (₹) Number of Persons 0-100   4 100-200    8 200-300      9 300-400     10  400-500    7  500-600     5 600-700     4  700-800    3

Summary:

The mean deviation about the mean for the given data is 157.92