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Home > Statistics > Grouped data > Population Variance, Standard deviation and coefficient of variation for grouped data calculator
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Population Variance, Standard deviation and coefficient of variation for grouped data calculator
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 1. Calculate the mean and standard deviation for the following distribution
| X |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
| f |
3 |
6 |
9 |
13 |
8 |
5 |
4 |
2. Calculate the mean and standard deviation for the following distribution
| Class |
10 - 20 |
20 - 30 |
30 - 40 |
40 - 50 |
50 - 60 |
60 - 70 |
70 - 80 |
| Frequency |
15 |
25 |
20 |
12 |
8 |
5 |
3 |
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Example (with steps)1. Calculate Population Variance `(sigma^2)` from the following grouped data
Solution:`x`
`(1)` | Frequency `(f)`
`(2)` | `f*x`
`(3)=(2)xx(1)` | `f*x^2=(f*x)xx(x)`
`(4)=(3)xx(1)` | | 0 | 1 | 0 | 0 | | 1 | 5 | 5 | 5 | | 2 | 10 | 20 | 40 | | 3 | 6 | 18 | 54 | | 4 | 3 | 12 | 48 | | --- | --- | --- | --- | | `n=25` | `sum f*x=55` | `sum f*x^2=147` |
Mean `bar x = (sum fx)/n` `=55/25` `=2.2`
Population Variance `sigma^2 = (sum f*x^2 - (sum f*x)^2/n)/n` `=(147 - (55)^2/25)/25` `=(147 - 121)/25` `=26/25` `=1.04`
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