1. Calculate Mean deviation about mode from the following grouped data
| Class-X | Frequency |
| 2 - 4 | 3 |
| 4 - 6 | 4 |
| 6 - 8 | 2 |
| 8 - 10 | 1 |
Solution:
Class
`(1)` | `f`
`(2)` | Mid value (`x`)
`(3)` | `|x-Z|=|x-4.6667|`
`(4)` | `f*|x-Z|`
`(5)=(2)xx(4)` |
| 2 - 4 | 3 | 3 | 1.6667 | 5 |
| 4 - 6 | 4 | 5 | 0.3333 | 1.3333 |
| 6 - 8 | 2 | 7 | 2.3333 | 4.6667 |
| 8 - 10 | 1 | 9 | 4.3333 | 4.3333 |
| --- | --- | --- | --- | --- |
| -- | `n=10` | -- | -- | `sum f*|x-Z|=15.3333` |
To find Mode Class
Here, maximum frequency is `4`.
`:.` The mode class is `4 - 6`.
`:. L = `lower boundary point of mode class `=4`
`:. f_1 = ` frequency of the mode class `=4`
`:. f_0 = ` frequency of the preceding class `=3`
`:. f_2 = ` frequency of the succedding class `=2`
`:. c = ` class length of mode class `=2`
`Z = L + ((f_1 - f_0) / (2*f_1 - f_0 - f_2)) * c`
`=4 + ((4 - 3)/(2*4 - 3 - 2)) * 2`
`=4 + (1/3) * 2`
`=4 + 0.6667`
`=4.6667`
Mean deviation of Mode
`delta bar x = (sum f*|x - Z|)/n`
`delta bar x = 15.3333/10`
`delta bar x = 1.5333`
Coefficient of Mean deviation `=(delta bar x)/(bar x)`
`=1.5333/4.6667`
`=0.3286`
2. Calculate Mean deviation about mode from the following grouped data
| Class-X | Frequency |
| 10 - 20 | 15 |
| 20 - 30 | 25 |
| 30 - 40 | 20 |
| 40 - 50 | 12 |
| 50 - 60 | 8 |
| 60 - 70 | 5 |
| 70 - 80 | 3 |
Solution:
Class
`(1)` | `f`
`(2)` | Mid value (`x`)
`(3)` | `|x-Z|=|x-26.6667|`
`(4)` | `f*|x-Z|`
`(5)=(2)xx(4)` |
| 10 - 20 | 15 | 15 | 11.6667 | 175 |
| 20 - 30 | 25 | 25 | 1.6667 | 41.6667 |
| 30 - 40 | 20 | 35 | 8.3333 | 166.6667 |
| 40 - 50 | 12 | 45 | 18.3333 | 220 |
| 50 - 60 | 8 | 55 | 28.3333 | 226.6667 |
| 60 - 70 | 5 | 65 | 38.3333 | 191.6667 |
| 70 - 80 | 3 | 75 | 48.3333 | 145 |
| --- | --- | --- | --- | --- |
| -- | `n=88` | -- | -- | `sum f*|x-Z|=1166.6667` |
To find Mode Class
Here, maximum frequency is `25`.
`:.` The mode class is `20 - 30`.
`:. L = `lower boundary point of mode class `=20`
`:. f_1 = ` frequency of the mode class `=25`
`:. f_0 = ` frequency of the preceding class `=15`
`:. f_2 = ` frequency of the succedding class `=20`
`:. c = ` class length of mode class `=10`
`Z = L + ((f_1 - f_0) / (2*f_1 - f_0 - f_2)) * c`
`=20 + ((25 - 15)/(2*25 - 15 - 20)) * 10`
`=20 + (10/15) * 10`
`=20 + 6.6667`
`=26.6667`
Mean deviation of Mode
`delta bar x = (sum f*|x - Z|)/n`
`delta bar x = 1166.6667/88`
`delta bar x = 13.2576`
Coefficient of Mean deviation `=(delta bar x)/(bar x)`
`=13.2576/26.6667`
`=0.4972`
This material is intended as a summary. Use your textbook for detail explanation.
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