Arithmetic Mean

A measure of central tendency condenses a whole set of data into a single, representative value — the "typical" figure around which the observations cluster. The three most commonly used averages are the arithmetic mean, the median and the mode (two others, the geometric mean and harmonic mean, exist for special situations but are not discussed here).

The arithmetic mean is the most widely used of these. It is defined as the sum of the values of all observations divided by the number of observations, and is written $\bar{X}$.

If there are $N$ observations $X_1, X_2, X_3, \ldots, X_N$, then:

where $\sum X$ is the total of all observations and $N$ is the number of observations.

A quick illustration. The monthly incomes (in Rs) of six families are 1600, 1500, 1400, 1525, 1625 and 1630. Adding these and dividing by 6: …