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.
| \(x_i\) | \(f_i\) | \(c.f\) |
| 15 | 3 | 3 |
| 21 | 5 | 8 |
| 27 | 6 | 14 |
| 30 | 7 | 21 |
| 35 | 8 | 29 |
Here, N = 29, which is odd.
∴ Median= \((\frac{29+1}{2})^{th}\) 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 \(|x_i-M|,\) are
| \(|x_i,M|\) | 15 | 9 | 3 | 0 | 5 |
| \(f_i\) | 3 | 5 | 6 | 7 | 8 |
| \(f_i|x-M|\) | 45 | 45 | 18 | 0 | 40 |
\(\sum_{I=1}^{5}f_i=29\) , \(\sum_{I=1}^{5}f_i|x_i-M|=148\)
\(=M.D.(M)=\frac{1}{N}\sum_{i=1}^{5}f_i|x_i-M|=\frac{1}{29}×148=5.1\)