Formula
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1. Mean deviation of Mean `delta bar x = (sum |x - bar x|)/n`
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2. Mean deviation of Median `delta bar x = (sum|x - M|)/n`
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3. Mean deviation of Mode `delta bar x = (sum|x - Z|)/n`
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Examples
1. Find Mean deviation about MEAN from the following data
`85,96,76,108,85,80,100,85,70,95`
Solution:
Mean `bar x = (sum x)/n`
`=(85 + 96 + 76 + 108 + 85 + 80 + 100 + 85 + 70 + 95)/10`
`=880/10`
`=88`
| `x` | `|x - bar x| = |x - 88|` |
| 85 | 3 `|85-88|=3`
`|x - 88|` |
| 96 | 8 `|96-88|=8`
`|x - 88|` |
| 76 | 12 `|76-88|=12`
`|x - 88|` |
| 108 | 20 `|108-88|=20`
`|x - 88|` |
| 85 | 3 `|85-88|=3`
`|x - 88|` |
| 80 | 8 `|80-88|=8`
`|x - 88|` |
| 100 | 12 `|100-88|=12`
`|x - 88|` |
| 85 | 3 `|85-88|=3`
`|x - 88|` |
| 70 | 18 `|70-88|=18`
`|x - 88|` |
| 95 | 7 `|95-88|=7`
`|x - 88|` |
| --- | --- |
| 880 | 94 |
Mean deviation of Mean
`delta bar x = (sum |x - bar x|)/n`
`delta bar x = 94/10`
`delta bar x = 9.4`
2. Find Mean deviation about MEAN from the following data
`69,66,67,69,64,63,65,68,72`
Solution:
Mean `bar x=(sum x)/n`
`=(69+66+67+69+64+63+65+68+72)/9`
`=603/9`
`=67`
| `x` | `|x - bar x| = |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 Mean
`delta bar x = (sum |x - bar x|)/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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