Example · High school
Terms
| Term | This example | Why |
|---|
| variance |
$\sigma^2 = 1/150 \approx 0.0067$ m$^2$
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The variance of the heights $1.6$, $1.7$, and $1.8$ m is the average of the squared differences from the mean $1.7$ m:
\[\sigma^2 = \frac{(-0.1)^2 + 0^2 + 0.1^2}{3} = \frac{0.02}{3} = \frac{1}{150} \approx 0.0067 \ \mathrm{m}^2.\]
The variance is in square meters, because the differences are squared.
|
| standard deviation |
$\sigma = \sqrt{6}/30 \approx 0.082$ m
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The standard deviation of the heights $1.6$, $1.7$, and $1.8$ m is the square root of the variance:
\[\sigma = \sqrt{\frac{1}{150}} = \frac{\sqrt{6}}{30} \approx 0.082 \ \mathrm{m}.\]
The standard deviation is in meters, like the heights.
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Distinctions using this example
- Variance vs. standard deviation: The heights have variance about $0.0067$ square meters but standard deviation about $0.082$ m, which is directly comparable with the heights themselves.
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