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Home > Statistical Methods calculators > Sample Variance, Standard deviation and coefficient of variation for ungrouped data example
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Sample Variance Example for ungrouped data
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- Formula & Example
- Sample Variance Example
- Sample Standard deviation Example
- Sample 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, Coefficient of Mean deviation
- Quartile deviation, Coefficient of QD, Interquartile range
- Decile deviation, Coefficient of DD, Interdecile range
- Percentile deviation, Coefficient of PD, Interpercentile range
- 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. Sample Variance Example
1. Calculate Sample Variance `(S^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`
Sample Variance `S^2 = (sum x^2 - (sum x)^2/n)/(n-1)` `=(569 - (53)^2/7)/6` `=(569 - 401.2857)/6` `=167.7143/6` `=27.9524`
2. Calculate Sample Variance `(S^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`
Sample Variance `S^2 = (sum (x - bar x)^2)/(n-1)` `=3000/7` `=428.5714`
3. Calculate Sample Variance `(S^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`
Sample Variance `S^2 = (sum (x - bar x)^2)/(n-1)` `=1216/9` `=135.1111`
This material is intended as a summary. Use your textbook for detail explanation. Any bug, improvement, feedback then
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