Harmonic mean is a statistical technique used to relate the average of two or more values by taking the reciprocals of those values and then finding the average of the reciprocals. This method is the inverse of the arithmetic mean, which is the traditional way of averaging values.

For example, in finance where it is common to represent the value of a company in terms of multiples such as price-to-earnings or price-to-sales ratios, harmonic mean can be used to find an average of those multiples that better reflects the underlying business conditions. The same approach would be employed by a market technician who may also use harmonic mean to identify patterns in a price chart such as a series of Fibonacci retracements.

Harmonic means are widely used in mathematics, physics, engineering, and economics, as well as in areas such as acoustics and mass media, and in settings related to machine learning and artificial intelligence. Generally, harmonic means should be used in cases where all values included in the calculation have similar values, like multiples, or when one of the values can be a large outlier compared to the others.

In order to calculate a harmonic mean, you first need to convert the data to its reciprocal and then average them. For example, if you are trying to calculate the harmonic mean of the values 1 and 4, you would first find their reciprocals, which would be 1 and 0.25. You would then take the average of those two values, which would be 0.625.

Harmonic means are useful for finding an average when working with similar values or when one of the values is an outlier, because it gives more weight to the smaller values and filters out the outliers. Harmonic Mean is also especially useful in engineering fields that are concerned with acoustic engineering, or any field that deals with vibration, and in calculating electricity or power consumption. It can also be used in cost analysis and in analysis of investments, and is sometimes used to measure disparities in income.

In conclusion, harmonic mean is a statistical calculation that can be used to calculate the average of two or more values. It is the reciprocal of the traditional arithmetic mean, and can be used when all values have similar values, or when one of the values is an outlier compared to the others. It is useful in engineering fields that are concerned with acoustics and vibration, as well as in cost analysis, investments, and income disparities.