Find the mean deviation about median for the following data:
Marks              0-10 10-20 20-30 30-40 40-50 50-60
Number of Girls     6        8        14      16      4        2

Solution:

Let us draw the table based on the given information.

Marks	No. of girls	c.f.	Mid-point (xi)	xi - M	fi xi - M
0 - 10	6	6	5	22.85	137.1
10 - 20	8	14	15	12.85	102.8
20 - 30	14	28	25	2.85	39.9
30 - 40	16	44	35	7.15	114.4
40 - 50	4	48	45	17.15	68.6
50 - 60	2	50	55	27.15	54.3
	50				517.1

Here,

N = ⁶∑_{i = 1} f_i = 50 and ⁶∑_{i = 1} f_i|x_i - M| = 517.1

l = 20, C = 14, f = 14, h = 10, N = 50

Median,

= (l + (N/2 - C))f' × h

= 20 + (25 - 14)/14 × 10

= 20 + 7.85

= 27.85

Hence,

the mean deviation about the median

M.D. (M) = 1/N ⁶∑_{i = 1} f_i|x_i - M|

= 1/50 × 517.1

= 10.34

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NCERT Solutions Class 11 Maths Chapter 15 Exercise 15.1 Question 11

Find the mean deviation about median for the following data: Marks   0-10 10-20 20-30 30-40 40-50 50-60 Number of Girls     6        8        14      16      4        2

Summary:

The mean deviation about the median for the given data is 10.34