Question -
Answer -
(i)┬аFindthe mean deviation from the median
Let us arrange the data in ascending order,
15.2, 27.9, 30.2, 32.5, 40.0, 52.3, 52.8, 55.2, 72.9, 79.0
We know that,
MD=
Where, |di| = |xi┬атАУ M|
The number of observations are Even then Median┬а=(40+52.3)/2 = 46.15
Median = 46.15
Number of observations, тАШnтАЩ = 10
| xi | |di| = |xi┬атАУ 46.15| |
| 40.0 | 6.15 |
| 52.3 | 6.15 |
| 55.2 | 9.05 |
| 72.9 | 26.75 |
| 52.8 | 6.65 |
| 79.0 | 32.85 |
| 32.5 | 13.65 |
| 15.2 | 30.95 |
| 27.9 | 19.25 |
| 30.2 | 15.95 |
| Total | 167.4 |
MD=
= 1/10 ├Ч 167.4
= 16.74
тИ┤ TheMean Deviation is 16.74.
(ii)┬аFindthe mean deviation from the mean also.
We know that,
MD=
Where, |di| = |xi┬атАУ x|
So, let тАШxтАЩ be the mean of the given observation.
x = [40.0 + 52.3 + 55.2 + 72.9 + 52.8 + 79.0 + 32.5 + 15.2 +27.9 + 30.2]/10
= 458/10
= 45.8
Number of observations, тАШnтАЩ = 10
| xi | |di| = |xi┬атАУ 45.8| |
| 40.0 | 5.8 |
| 52.3 | 6.5 |
| 55.2 | 9.4 |
| 72.9 | 27.1 |
| 52.8 | 7 |
| 79.0 | 33.2 |
| 32.5 | 13.3 |
| 15.2 | 30.6 |
| 27.9 | 17.9 |
| 30.2 | 15.6 |
| Total | 166.4 |
MD=
= 1/10 ├Ч 166.4
= 16.64
тИ┤ The┬аMean Deviation is 16.64