1. Calculate Mean deviation about mode from the following grouped data
| X | Frequency |
| 10 | 3 |
| 11 | 12 |
| 12 | 18 |
| 13 | 12 |
| 14 | 3 |
Solution:
`x`
`(1)` | `f`
`(2)` | `|x-Z|=|x-12|`
`(3)` | `f*|x-Z|`
`(4)=(2)xx(3)` |
| 10 | 3 | 2 | 6 |
| 11 | 12 | 1 | 12 |
| 12 | 18 | 0 | 0 |
| 13 | 12 | 1 | 12 |
| 14 | 3 | 2 | 6 |
| --- | --- | --- | --- |
| -- | `n=48` | -- | `sum f*|x-Z|=36` |
Mode :
the frequency of observation `12` is maximum (`18`)
`:. Z = 12`
Mean deviation of Mode
`delta bar x = (sum f*|x - Z|)/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 mode from the following grouped data
Solution:
`x`
`(1)` | `f`
`(2)` | `|x-Z|=|x-2|`
`(3)` | `f*|x-Z|`
`(4)=(2)xx(3)` |
| 0 | 1 | 2 | 2 |
| 1 | 5 | 1 | 5 |
| 2 | 10 | 0 | 0 |
| 3 | 6 | 1 | 6 |
| 4 | 3 | 2 | 6 |
| --- | --- | --- | --- |
| -- | `n=25` | -- | `sum f*|x-Z|=19` |
Mode :
the frequency of observation `2` is maximum (`10`)
`:. Z = 2`
Mean deviation of Mode
`delta bar x = (sum f*|x - Z|)/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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