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Method and examples
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Method
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Find Population Variance, Standard deviation and coefficient of variation for ungrouped data
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Enter Data
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Standard deviation using Direct method or Assumed mean method
Method
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- `85,96,76,108,85,80,100,85,70,95`
- `3,13,11,15,5,4,2`
- `3,23,13,11,15,5,4,2`
- `69,66,67,69,64,63,65,68,72`
- `4,14,12,16,6,3,1,2,3`
- `73,70,71,73,68,67,69,72,76,71`
- `10,50,30,20,10,20,70,30`
- `21,23,19,17,12,15,15,17,17,19,23,23,21,23,25,25,21,19,19,19`
- `2,3,7,8,8,5,5,3,7,3,1,8,6,7,4,5,6,3,2,4,3,4,9,8,3`
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Decimal Place =
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log(x)/ln(x) Option for Geometric mean =
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Solution
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Solution provided by AtoZmath.com
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Population Variance, Standard deviation and coefficient of variation for ungrouped data calculator
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 1. 85,96,76,108,85,80,100,85,70,95
2. 3,13,11,11,5,4,2
3. 3,23,13,11,15,3,5,4,2
4. 69,66,67,69,64,63,65,68,72
5. 4,14,12,16,6,3,1,2,3
6. 73,70,71,73,68,67,69,72,76,71
7. 10,50,30,20,10,20,70,30
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Example1. Calculate Population Variance `(sigma^2)` from the following data
`3,13,11,15,5,4,2`Solution:| `x` | `x^2` | | 3 | 9 | | 13 | 169 | | 11 | 121 | | 15 | 225 | | 5 | 25 | | 4 | 16 | | 2 | 4 | | --- | --- | | `sum x=53` | `sum x^2=569` |
Mean `bar x=(sum x)/n` `=(3+13+11+15+5+4+2)/7` `=53/7` `=7.5714`
Population Variance `sigma^2 = (sum x^2 - (sum x)^2/n)/n` `=(569 - (53)^2/7)/7` `=(569 - 401.2857)/7` `=167.7143/7` `=23.9592`
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