Page No 360:
Question 8:
Find the mean deviation about the median for the data
xi | 15 | 21 | 27 | 30 | 35 |
fi | 3 | 5 | 6 | 7 | 8 |
The given observations are already in ascending order.
Adding a column corresponding to cumulative frequencies of the given data, we obtain the following table.
xi | fi | c.f. |
15 | 3 | 3 |
21 | 5 | 8 |
27 | 6 | 14 |
30 | 7 | 21 |
35 | 8 | 29 |
Here, N = 29, which is odd.
observation = 15th observation
This observation lies in the cumulative frequency 21, for which the corresponding observation is 30.
∴ Median = 30
The absolute values of the deviations from median, i.e.
are
|xi – M| | 15 | 9 | 3 | 0 | 5 |
fi | 3 | 5 | 6 | 7 | 8 |
fi |xi – M| | 45 | 45 | 18 | 0 | 40 |
∴ 
