Weighted Arithmetic Mean

HISTORY

The weighted arithmetic mean was introduced by Cotes, Roger in 1712. His work was published in 1722, six years after his death.

MATHEMATICAL ASPECTS

Let ${ x_1,x_2,\ldots,x_n }$ be a set of n quantities or n observations relative to a quantitative variable X to which we assign the weights ${ w_1,w_2,\ldots,w_n }$.

The weighted arithmetic mean equals:

$$ \bar{x} = \frac{\sum\limits_{i=1}^n x_i \cdot w_i}{\sum\limits_{i=1}^n w_i}\:. $$

DOMAINS AND LIMITATIONS

The weighted arithmetic mean is now used in economics, especially in consumer and producer price indices, etc.

EXAMPLES

Suppose that...