3. Mean deviation about median example
1. Find Mean deviation about MEDIAN from the following data
`73,70,71,73,68,67,69,72,76,71`
Solution:
Median :
Observations in the ascending order are :
`67,68,69,70,71,71,72,73,73,76`
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`
`=(71 + 71)/2`
`=71`
| `x` | `|x - M| = |x - 71|` | | 73 | 2 | | 70 | 1 | | 71 | 0 | | 73 | 2 | | 68 | 3 | | 67 | 4 | | 69 | 2 | | 72 | 1 | | 76 | 5 | | 71 | 0 | | --- | --- | | 710 | 20 |
Mean deviation of Median
`delta bar x = (sum |x - M|)/n`
`delta bar x = 20/10`
`delta bar x = 2`
Coefficient of Mean deviation `=(delta bar x)/(bar x)`
`=2/71`
`=0.0282`
2. Find Mean deviation about MEDIAN from the following 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.
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