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Properties of the standard deviation:
Properties of the standard deviation:
- s ≥ 0 for any data set.
-If s = 0 then the data has no variability so all of the observations must be equal to the mean.
- The larger s is the more variability in the data set (i.e. the further the observations lie from the mean).
- The standard deviation, s, as well as the variance, , are sensitive to extreme values.
- One prefers to use the standard deviation, s, as a measure of spread instead of the variance because s is measured in the same units as the original data.
- If one uses the sample mean, , to measure the center of the distribution, s is the appropriate measure of spread to use with the mean.