# Harmonic Mean definition, formula and applications

## Definition

The harmonic mean is the inverse of the arithmetic mean of the reciprocals of the observations of a set. The formula for harmonic mean is,

where, H= Harmonic mean

n= number of observations

i=1,2,3,...,n.

### When to use Harmonic mean

The harmonic mean is suitable when the values are pertaining to the rate of change per unit time, such as speed, number of hems produced per day, contracts completed per year, etc. In general, the harmonic mean is suitable for time, speed, rates, prices, etc.

### Advantages of the harmonic mean

There are some merits of harmonic mean-

• Harmonic mean is based on all observations of a set.
• It is a good mean for a highly variable series.
• It gives more weightage to the small values and leas weightage to the large value.
• It is better than the weighted mean since, in this, values are automatically weighted.

### Disadvantages of the harmonic mean

There are some demerits of harmonic mean-

• Harmonic mean calculation is complicated.
• If any value is zero, it cannot be calculated.
• Its value is generally not a member of the
• series.