Question

what are the mathematical properties of standard deviations
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Answer 1

Properties of standard deviation

Standard deviation is never negative. Standard deviation is sensitive to outliers. A single outlier can raise the standard deviation and in turn, distort the picture of spread. For data with approximately the same mean, the greater the spread, the greater the standard deviation.

Answer 2

Hey!!

Here is your answer -

1. It is the measure of the spread of the distribution around the central value i.e. mean. E.g. for two distributions with approximately same means, the one with higher S.D. is more spread around the mean
2. It is never negative (makes sense)
3. It is affected by outliers. (since it is dependent on mean which is turn sensitive to outliers)
4. It is used for comparing two distributions. E.g. for two distributions with unequal mean and S.D., the ratio mean/S.D. is used for comparing the two.