Probably most commonly to get the average of rates. For example to average speeds in km/h.

I suppose another use would be to express averages in the original units for data that had been reciprocal transformed for analysis.

The harmonic mean (HM) of a set of data may be defined as the reciprocal of the mean of the reciprocals of the data. Where there is inverse variation or relationship the HM might be used as an average. For example in the weighted least squares technique the weights are inverses of the corresponding variances. Averaging such weights could involve the use of the HM.

The harmonic mean (HM) of a set of data may be defined as the reciprocal of the mean of the reciprocals of the data. Where there is inverse variation or relationship the HM might be used as an average. For example in the weighted least squares technique the weights are inverses of the corresponding variances. Averaging such weights could involve the use of the HM.

Harmonic mean is another measure of central tendency and is also based on mathematics like arithmetic mean and geometric mean. Like arithmetic mean and geometric mean, harmonic mean is also useful for quantitative data.

In certain situations, especially many situations involving rates and ratios,

the harmonic mean provides the truest average.

1 - For example, in first test a typist types 400 words in 50 minutes, in second test he types the same words (400) in 40 minutes and in third test he takes 30 minutes to type the 400 words. Then average time of typing can be calculated by harmonic mean.

2 - For instance, if a vehicle travels a certain distance d at a speed x (60 km/h) and then the same distance again at a speed y (40 km/h), then its average speed is the harmonic mean of x and y (48 km/h).

3 - The weighted harmonic mean is the preferable method for averaging multiples, such as the price–earnings ratio (P/E), in which price is in the numerator.

4 - In any triangle, the radius of the in circle is one-third of the harmonic mean of the altitudes.

The harmonic mean could be used if companies are to be valued by multiples like the price earnings ratio (PE ratio). It can be shown that by using an average PE ratio, one implicitly assumes different levels of investment. By using the harmonic mean, one assumes that the same amount is invested in each of the comparable companies. Because the latter assumption is more plausible, the harmonic mean should be used (for example see Preprint Valuation with multiples: averaging, links, aggregation, and...

Hello

Harmonic mean for calculating mean data is obtained by combining two scales.

In particular cases, especially those involving rates and ratios, the harmonic mean gives the most correct value of the mean. For example, if a vehicle travels a specified distance at speed x (eg 60 km / h) and then travels again at the speed y (e.g.40 km / h), the average speed value is the harmonic mean x, y (Ie, 48 km / h).