The harmonic mean is a type of average that is particularly useful for sets of numbers that are defined in relation to some unit, such as speed or rates. It is calculated by taking the reciprocal of the average of the reciprocals of the numbers in the set. The formula for the harmonic mean of a set of values x₁, x₂, ..., xₙ is given by H = \fracn\frac{1x₁ + \frac1x₂ + ... + \frac1xₙ} , where n is the total number of values. This mean is often used in situations where average rates are desired, such as in calculating average speeds over a distance. For example, if a car travels a certain distance at different speeds, the harmonic mean provides a more accurate average speed than the arithmetic mean. It is particularly effective when the values vary widely, as it tends to minimize the impact of