Find the mean deviation about the median for the following data :
class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
Frequency | 6 | 7 | 15 | 16 | 4 | 2 |
we make the following table from the given data:
class | Frequency fi | Cumulative frequency c.f | Mid-points xi |
0-10 | 6 | 6 | 5 |
10-20 | 7 | 13 | 15 |
20-30 | 15 | 28 | 25 |
30-40 | 16 | 44 | 35 |
40-50 | 4 | 48 | 45 |
50-60 | 2 | 50 | 55 |
50 |
The class interval containing or 25th item is 20-30. Therefore, 20–30 is the median class. We know that
Here, l = 20, C = 13, f = 15, h = 10 and N = 50
Therefore,
Now,
class | Frequency fi | Cumulative frequency c.f | Mid-points xi | |xi-M| | fi |xi-M| |
0-10 | 6 | 6 | 5 | 23 | 138 |
10-20 | 7 | 13 | 15 | 13 | 91 |
20-30 | 15 | 28 | 25 | 3 | 45 |
30-40 | 16 | 44 | 35 | 7 | 112 |
40-50 | 4 | 48 | 45 | 17 | 68 |
50-60 | 2 | 50 | 55 | 27 | 54 |
50 | 508 |
We have, and