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 median from the following grouped data
| X | Frequency |
| 10 | 3 |
| 11 | 12 |
| 12 | 18 |
| 13 | 12 |
| 14 | 3 |
Solution:
`x`
`(1)` | `f`
`(2)` | `cf`
`(3)` | `|x-M|=|x-12|`
`(4)` | `f*|x-M|`
`(5)=(2)xx(4)` |
| 10 | 3 | 3 `3=0+3`
`(3)=`Previous `(3)+(2)` | 2 `|x - 12|=|10-12|=2` | 6 `6=3xx2`
`(5)=(2)xx(4)` |
| 11 | 12 | 15 `15=3+12`
`(3)=`Previous `(3)+(2)` | 1 `|x - 12|=|11-12|=1` | 12 `12=12xx1`
`(5)=(2)xx(4)` |
| 12 | 18 | 33 `33=15+18`
`(3)=`Previous `(3)+(2)` | 0 `|x - 12|=|12-12|=0` | 0 `0=18xx0`
`(5)=(2)xx(4)` |
| 13 | 12 | 45 `45=33+12`
`(3)=`Previous `(3)+(2)` | 1 `|x - 12|=|13-12|=1` | 12 `12=12xx1`
`(5)=(2)xx(4)` |
| 14 | 3 | 48 `48=45+3`
`(3)=`Previous `(3)+(2)` | 2 `|x - 12|=|14-12|=2` | 6 `6=3xx2`
`(5)=(2)xx(4)` |
| --- | --- | --- | --- | --- |
| -- | `n=48` | -- | -- | `sum f*|x-M|=36` |
Median :
M = value of `(n/2)^(th)` observation
= value of `(48/2)^(th)` observation
= value of `24^(th)` observation
From the column of cumulative frequency `cf`, we find that the `24^(th)` observation is `12`.
Hence, the median of the data is `12`.
Mean deviation of Median
`delta bar x = (sum f*|x - M|)/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 median from the following grouped data
Solution:
`x`
`(1)` | `f`
`(2)` | `cf`
`(3)` | `|x-M|=|x-2|`
`(4)` | `f*|x-M|`
`(5)=(2)xx(4)` |
| 0 | 1 | 1 | 2 | 2 |
| 1 | 5 | 6 | 1 | 5 |
| 2 | 10 | 16 | 0 | 0 |
| 3 | 6 | 22 | 1 | 6 |
| 4 | 3 | 25 | 2 | 6 |
| --- | --- | --- | --- | --- |
| -- | `n=25` | -- | -- | `sum f*|x-M|=19` |
Median :
M = value of `((n+1)/2)^(th)` observation
= value of `(26/2)^(th)` observation
= value of `13^(th)` observation
From the column of cumulative frequency `cf`, we find that the `13^(th)` observation is `2`.
Hence, the median of the data is `2`.
Mean deviation of Median
`delta bar x = (sum f*|x - M|)/n`
`delta bar x = 19/25`
`delta bar x = 0.76`
Coefficient of Mean deviation `=(delta bar x)/(bar x)`
`=0.76/2`
`=0.38`
This material is intended as a summary. Use your textbook for detail explanation.
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