How is harmonic mean used in statistics?

Harmonic mean is a type of average that is calculated by dividing the number of values in a data series by the sum of the reciprocals (1/x_i) of each value in the data series. The harmonic mean is often used to calculate the average of the ratios or rates.

Is harmonic mean greater than arithmetic mean?

& (2) Harmonic mean is always lower than arithmetic mean and geometric mean. only if the values (or the numbers or the observations) whose means are to calculated are real and strictly positive.

What does the term harmonic mean?

reciprocal of
: the reciprocal of the arithmetic mean of the reciprocals of a finite set of numbers.

What is the difference between harmonic mean and arithmetic mean?

The difference between the harmonic mean and arithmetic mean is that the arithmetic mean is appropriate when the values have the same units whereas the harmonic mean is appropriate when the values are the ratios of two variables and have different measures.

What are the advantages of harmonic mean?

The harmonic mean has the following merits. It is rigidly defined. It is based on all the observations of a series i.e. it cannot be calculated ignoring any item of a series. It is capable of further algebraic treatment. It gives better result when the ends to be achieved are the same for the different means adopted.

Why harmonic mean is used in F1 score?

The F1 score is the harmonic mean of precision and recall taking both metrics into account in the following equation: We use the harmonic mean instead of a simple average because it punishes extreme values. A classifier with a precision of 1.0 and a recall of 0.0 has a simple average of 0.5 but an F1 score of 0.

Why is harmonic mean lower than arithmetic mean?

Relationship with other means For all positive data sets containing at least one pair of nonequal values, the harmonic mean is always the least of the three means, while the arithmetic mean is always the greatest of the three and the geometric mean is always in between.

Can harmonic mean be negative?

The harmonic mean does not take rates with a negative or zero value, e.g. all rates must be positive.

Is harmonic mean affected by extreme values?

It is not affected by extreme values.

What is harmonic mean advantages and disadvantages?

It is capable of further algebraic treatment. It gives better result when the ends to be achieved are the same for the different means adopted. It gives the greatest weight to the smallest item of a series. It can be calculated even when a series contains any negative value. It makes a skewed distribution a normal one.

What are the disadvantages of harmonic mean?

The demerits of the harmonic series are as follows: The harmonic mean is greatly affected by the values of the extreme items. It cannot be able to calculate if any of the items is zero. The calculation of the harmonic mean is cumbersome, as it involves the calculation using the reciprocals of the number.

What is harmonic mean of precision and recall?

Harmonic mean is a type of average generally used for numbers that represent a rate or ratio such as the precision and the recall in information retrieval. The harmonic mean can be described as the reciprocal of the arithmetic mean of the reciprocals of the data.

How do you calculate harmonic?

To calculate the harmonic mean for a set of a data, all of the individual elements are averaged and divided by the sum of the reciprocals of the elements. The formula for calculating harmonic mean is: N / (1/a1 + 1/a2 + 1/a3 + 1/a4 + ……. +1/aN) where N is the total sample size of your data.

What does harmonic mean in math?

Harmonic mean. In mathematics, the harmonic mean (sometimes called the subcontrary mean) is one of several kinds of average, and in particular one of the Pythagorean means. Typically, it is appropriate for situations when the average of rates is desired.

What is an example of a harmonic?

An example of simple harmonic motion is the swing in the playground, or a something swinging on a rope. A weight on a spring bouncing up and down is simple harmonic motion, because energy is less likely to be lost in each turning of the wave.

What is a harmonic equation?

The equation of a simple harmonic motion is: where x is the displacement, A is the amplitude of oscillation, f is the frequency, t is the elapsed time, and f is the phase of oscillation.