Formula
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1. Mean deviation of Mean `delta bar x = (sum f*|x - bar x|)/n`
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2. Mean deviation of Mean `delta bar x = (sum f*|x - M|)/n`
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3. Mean deviation of Mode `delta bar x = (sum f*|x - Z|)/n`
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Examples
1. Calculate Mean deviation about mean from the following grouped data
| X | Frequency |
| 10 | 3 |
| 11 | 12 |
| 12 | 18 |
| 13 | 12 |
| 14 | 3 |
Solution:
`x`
`(1)` | `f`
`(2)` | `f*x`
`(3)=(2)xx(1)` | `|x-bar x|=|x-12|`
`(4)` | `f*|x-bar x|`
`(5)=(2)xx(4)` |
| 10 | 3 | 30 `30=3xx10`
`(3)=(2)xx(1)` | 2 `|x - 12|=|10-12|=2` | 6 `6=3xx2`
`(5)=(2)xx(4)` |
| 11 | 12 | 132 `132=12xx11`
`(3)=(2)xx(1)` | 1 `|x - 12|=|11-12|=1` | 12 `12=12xx1`
`(5)=(2)xx(4)` |
| 12 | 18 | 216 `216=18xx12`
`(3)=(2)xx(1)` | 0 `|x - 12|=|12-12|=0` | 0 `0=18xx0`
`(5)=(2)xx(4)` |
| 13 | 12 | 156 `156=12xx13`
`(3)=(2)xx(1)` | 1 `|x - 12|=|13-12|=1` | 12 `12=12xx1`
`(5)=(2)xx(4)` |
| 14 | 3 | 42 `42=3xx14`
`(3)=(2)xx(1)` | 2 `|x - 12|=|14-12|=2` | 6 `6=3xx2`
`(5)=(2)xx(4)` |
| --- | --- | --- | --- | --- |
| -- | `n=48` | `sum f*x=576` | -- | `sum f*|x-bar x|=36` |
Mean `bar x=(sum f x)/n`
`=576/48`
`=12`
Mean deviation of Mean
`delta bar x = (sum f*|x - bar x|)/n`
`delta bar x = 36/48`
`delta bar x = 0.75`
Coefficient of Mean deviation `=(delta bar x)/(bar x)`
`=0.75/12`
`=0.0625`
2. Calculate Mean deviation about mean from the following grouped data
Solution:
`x`
`(1)` | `f`
`(2)` | `f*x`
`(3)=(2)xx(1)` | `|x-bar x|=|x-2.2|`
`(4)` | `f*|x-bar x|`
`(5)=(2)xx(4)` |
| 0 | 1 | 0 | 2.2 | 2.2 |
| 1 | 5 | 5 | 1.2 | 6 |
| 2 | 10 | 20 | 0.2 | 2 |
| 3 | 6 | 18 | 0.8 | 4.8 |
| 4 | 3 | 12 | 1.8 | 5.4 |
| --- | --- | --- | --- | --- |
| -- | `n=25` | `sum f*x=55` | -- | `sum f*|x-bar x|=20.4` |
Mean `bar x=(sum f x)/n`
`=55/25`
`=2.2`
Mean deviation of Mean
`delta bar x = (sum f*|x - bar x|)/n`
`delta bar x = 20.4/25`
`delta bar x = 0.816`
Coefficient of Mean deviation `=(delta bar x)/(bar x)`
`=0.816/2.2`
`=0.3709`
This material is intended as a summary. Use your textbook for detail explanation.
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