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} . This mean is often used in situations where rates are involved, such as calculating average speeds. 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 emphasizes smaller values more than larger ones, making it suitable for datasets where lower values are more significant, such as in finance or physics.