harmonic mean
harmonic average

The harmonic mean, on the other hand, gives equal weight to each data point.

The harmonic mean is a special case where all of the weights are equal to 1.

For a random sample the harmonic mean is calculated as above.

Then the effective population size is the harmonic mean of these, giving:

The harmonic mean is very sensitive to low values.

Similarly, the harmonic mean is lower than the geometric mean.

It is also equivalent to any weighted harmonic mean where all weights are equal.

In geophysical reservoir engineering studies, the harmonic mean is widely used.

The focus so determined would be about 1.3 m, the approximate harmonic mean of the near and far distances.

Harmonic mean for a non-empty collection of numbers a, a, .

The harmonic mean tends to be dominated by the smallest bottleneck that the population goes through.

The F-score is the harmonic mean of precision and recall:

Being proportional to the harmonic mean of A and B, this formula has several applications.

In this scenario, using the arithmetic or harmonic mean would change the ranking of the results depending on what is used as a reference.

Another example of a weighted mean is the weighted harmonic mean.

This also equals n times the inverse of the harmonic mean of these natural numbers.

This problem can be overcome by taking instead the expectation of the harmonic mean ( 1 / "x" ).

(It is the harmonic mean of the two totals.)

This equality follows from the following symmetry displayed between both harmonic means:

Then "s" equals half the harmonic mean of "c" and "t".

If we take to be the set of positive real numbers and , then the f-mean corresponds to the harmonic mean.

The contraharmonic is the remainder of the diameter on which the harmonic mean lies.

It is possible to recursively calculate the harmonic mean (H) of n variates.

Now on the left we have the arithmetic mean and on the right the harmonic mean, so this inequality is true.

By means of the above expressions, the harmonic mean of the terms of a continued fraction may be obtained as well.

There is also a harmonic average of functions and a quadratic average (or root mean square) of functions.

For alternative dual-fuel vehicles, an assumption is made that the vehicles would operate 50% of the time on the alternative fuel and 50% of the time on conventional fuel, resulting in a fuel economy that is based on a harmonic average of alternative fuel and conventional fuel.