📉Variance vs Standard deviation📏
Both quantities measure how spread out data is, and they are directly related — the standard deviation is simply the square root of the variance.
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📉Variance
- ✓The average of the squared deviations from the mean
- ✓Always non-negative
- ✓Expressed in squared units of the original data
- ✓Adds neatly when combining independent variables
- ✓A core building block of statistical theory
📏Standard deviation
- ✓The square root of the variance
- ✓Expressed in the same units as the original data
- ✓Easier to interpret in real-world terms
- ✓Used to describe the width of a normal distribution
- ✓More common in reports and everyday statistics
Verdict
Variance is mathematically convenient but its squared units are hard to interpret. Standard deviation undoes the squaring, so it is easier to read. Use variance in proofs, standard deviation in reports.
Frequently asked
How are variance and standard deviation related?+
The standard deviation is the square root of the variance, bringing it back to the original units.
Why is standard deviation easier to interpret?+
It is in the same units as the data, so a deviation in meters or dollars makes intuitive sense.
Can variance be negative?+
No. Because it averages squared values, variance is always zero or positive.
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