Harmonic Mean

The harmonic mean is a type of average that is calculated by taking the reciprocal of each number in the data set and then averaging those reciprocals. The harmonic mean is often used when the data set contains a large number of zeros or negative values, as it is less affected by these values than other types of averages.

The harmonic mean is calculated using the following formula:

H = (n/(1/x1 + 1/x2 + … + 1/xn))

where:

• H is the harmonic mean
• n is the number of values in the data set
• x1, x2, ..., xn are the values in the data set

For example, if the data set is {1, 2, 3, 4, 5}, the harmonic mean would be calculated as follows:

H = (5/(1/1 + 1/2 + 1/3 + 1/4 + 1/5)) = 3

The harmonic mean is often used in finance to calculate the average return on an investment portfolio. This is because the harmonic mean is less affected by outliers than the arithmetic mean, which is the more commonly used type of average.

The harmonic mean can also be used to calculate the average speed of an object over a period of time. This is because the harmonic mean takes into account the time spent at each speed, which is not done by the arithmetic mean.

The harmonic mean is a useful tool for calculating averages when the data set contains a large number of zeros or negative values, or when it is important to take into account the time spent at each speed.