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Home > Statistical Methods calculators > Population Variance, Standard deviation and coefficient of variation for ungrouped data example
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Population Variance Example for ungrouped data
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- Formula & Example
- Population Variance Example
- Population Standard deviation Example
- Population coefficient of variation Example
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Other related methods
- Mean, Median and Mode
- Quartile, Decile, Percentile, Octile, Quintile
- Population Variance, Standard deviation and coefficient of variation
- Sample Variance, Standard deviation and coefficient of variation
- Population Skewness, Kurtosis
- Sample Skewness, Kurtosis
- Geometric mean, Harmonic mean
- Mean deviation, Quartile deviation, Decile deviation, Percentile deviation
- Five number summary
- Box and Whisker Plots
- Construct an ungrouped frequency distribution table
- Construct a grouped frequency distribution table
- Maximum, Minimum
- Sum, Length
- Range, Mid Range
- Stem and leaf plot
- Ascending order, Descending order
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2. Population Variance Example
1. 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`
2. Calculate Population Variance `(sigma^2)` from the following data
`10,50,30,20,10,20,70,30`
Solution:
| `x` | `x - bar x = x - 30` | `(x - bar x)^2` | | 10 | -20 | 400 | | 50 | 20 | 400 | | 30 | 0 | 0 | | 20 | -10 | 100 | | 10 | -20 | 400 | | 20 | -10 | 100 | | 70 | 40 | 1600 | | 30 | 0 | 0 | | --- | --- | --- | | `sum x=240` | `sum (x - bar x)=0` | `sum (x - bar x)^2=3000` |
Mean `bar x=(sum x)/n`
`=(10+50+30+20+10+20+70+30)/8`
`=240/8`
`=30`
Population Variance `sigma^2 = (sum (x - bar x)^2)/n`
`=3000/8`
`=375`
3. Calculate Population Variance `(sigma^2)` from the following data
`85,96,76,108,85,80,100,85,70,95`
Solution:
| `x` | `x - bar x = x - 88` | `(x - bar x)^2` | | 85 | -3 | 9 | | 96 | 8 | 64 | | 76 | -12 | 144 | | 108 | 20 | 400 | | 85 | -3 | 9 | | 80 | -8 | 64 | | 100 | 12 | 144 | | 85 | -3 | 9 | | 70 | -18 | 324 | | 95 | 7 | 49 | | --- | --- | --- | | `sum x=880` | `sum (x - bar x)=0` | `sum (x - bar x)^2=1216` |
Mean `bar x=(sum x)/n`
`=(85+96+76+108+85+80+100+85+70+95)/10`
`=880/10`
`=88`
Population Variance `sigma^2 = (sum (x - bar x)^2)/n`
`=1216/10`
`=121.6`
This material is intended as a summary. Use your textbook for detail explanation.
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