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Harmonic Mean

Statistical Glossary

Harmonic Mean:

Harmonic mean is a measure of central location. The harmonic mean Math image of Math image positive values Math image is defined by the formula

Let the path between two cities Math image and Math image be divided into Math image parts of equal length. One drives the Math image th part at velocity Math image . Then, the average speed on the whole journey is the harmonic mean Math image of velocities Math image .

The harmonic mean is sensitive to a single small value – Math image tends to be small if at least one of the values Math image is abnormally small. (In the above example, this corresponds to very slow driving through one of the road parts, leading you to spend most of the journey on this part of the path).

For this reason, the harmonic mean is often used, for example, to aggregate scores in different types of activity to a single final score, e.g. to estimate students´ performance. This ensure that no partial scores are radically lower than the final score.

See also Mean values (comparison) .

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