Professor Puzzler's Statistics CalculatorProvide a data set below, and find out all you need to know!Harmonic mean Detailed analysisAverageMedianModeRangeOutliersStandard deviationGeometric meanQuartilesIQRVariance
Harmonic MeanPlease enter data above to calculate the harmonic mean.
ExplanationThe harmonic mean is obtained by taking the reciprocals of each of the data points, and averaging all those points (adding them together and dividing by the number of points). Finally, since we began by taking reciprocals of the data points, we finish by taking the reciprocal of the result.
Harmonic means can be used as an alternate way of dealing with outliers, provided all the outliers are on the high side; if you have low outliers, using the harmonic mean will badly skew your results.
Under what circumstances does a data set not have a harmonic mean? If one or more of the data points is zero. This would result in a division by zero, which is not defined.
For more information about harmonic means, visit our reference unit on Pythagorean Means.
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