# Professor Puzzler's Statistics Calculator

Provide a data set below, and find out all you need to know!Standard deviation Detailed analysisAverageMedianModeRangeOutliersHarmonic meanGeometric meanQuartilesIQRVariance# Standard Deviation

*Please enter data above to calculate standard deviation.*

## Explanation

Standard deviation is a measure of how tightly grouped the data is around the mean, or average. A small standard deviation means that the data is tightly grouped, while I high standard deviation indicates that the data is more widely spread. A standard deviation of zero indicates that all the data points in the set are identical.Standard deviation is calcuated as follows. First, the average is calculated, and then each point's distance from the mean is calculated. These values are all squared and the squares are averaged. This quantity is known as the variance. To calculate the standard deviation from the variance, simply take the square root.

Note that, since the variance is measured in units which are the

*square*of the measured units, taking the square root means that the standard deviation shares the same units as the original data. Thus, if you are measuring distance in meters, the standard deviation is in meters as well.

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