1. Find Mean deviation about Median from the following ungrouped data
`85,96,76,108,85,80,100,85,70,95`Solution:Median :Observations in the ascending order are :
`70,76,80,85,85,85,95,96,100,108`
Here, `n=10` is even.
`M=(text{Value of } (n/2)^(th) text{ observation} + text{Value of } (n/2 + 1)^(th) text{ observation})/2`
`=(text{Value of } (10/2)^(th) text{ observation} + text{Value of } (10/2 + 1)^(th) text{ observation})/2`
`=(text{Value of }5^(th) text{ observation} + text{Value of }6^(th) text{ observation})/2`
`=(85 + 85)/2`
`=85`
| `x` | `|x - M| = |x - 85|` |
| 85 | 0 |
| 96 | 11 |
| 76 | 9 |
| 108 | 23 |
| 85 | 0 |
| 80 | 5 |
| 100 | 15 |
| 85 | 0 |
| 70 | 15 |
| 95 | 10 |
| --- | --- |
| `880` | `88` |
Mean deviation of Median
`delta bar x = (sum |x - M|)/n`
`delta bar x = 88/10`
`delta bar x = 8.8`
Coefficient of Mean deviation `=(delta bar x)/(bar x)`
`=8.8/85`
`=0.1035`
2. Find Mean deviation about Median from the following ungrouped data
`69,66,67,69,64,63,65,68,72`Solution:Median :Observations in the ascending order are :
`63,64,65,66,67,68,69,69,72`
Here, `n=9` is odd.
`M=` value of `((n+1)/2)^(th)` observation
`=` value of `((9+1)/2)^(th)` observation
`=` value of `5^(th)` observation
`=67`
| `x` | `|x - M| = |x - 67|` |
| 69 | 2 |
| 66 | 1 |
| 67 | 0 |
| 69 | 2 |
| 64 | 3 |
| 63 | 4 |
| 65 | 2 |
| 68 | 1 |
| 72 | 5 |
| --- | --- |
| `603` | `20` |
Mean deviation of Median
`delta bar x = (sum |x - M|)/n`
`delta bar x = 20/9`
`delta bar x = 2.2222`
Coefficient of Mean deviation `=(delta bar x)/(bar x)`
`=2.2222/67`
`=0.0332`
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then