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Question 11:
Find the mean deviation about median for the following data:
Marks | Number of girls |
0-10 | 6 |
10-20 | 8 |
20-30 | 14 |
30-40 | 16 |
40-50 | 4 |
50-60 | 2 |
The following table is formed.
Marks | Number of girls fi | Cumulative frequency (c.f.) | Mid-point xi | |xi – Med.| | fi |xi – Med.| |
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 |
The class interval containing the
or 25th item is 20 – 30.
Therefore, 20 – 30 is the median class.
It is known that,
Here, l = 20, C = 14, f = 14, h = 10, and N = 50
∴ Median =
Thus, mean deviation about the median is given by,
