# Weighted Arithmetic Mean

In calculation of arithmetic mean, the importance of all the items was considered to be equal. However, there may be situations in which all the items under considerations are not equal importance. For example, we want to find average number of marks per subject who appeared in different subjects like Mathematics, Statistics, Physics and Biology. These subjects do not have equal importance. If we find arithmetic mean by giving Mean. Thus, arithmetic mean computed by considering relative importance of each items is called weighted arithmetic mean. To give due importance to each item under consideration, we assign number called weight to each item in proportion to its relative importance.

Weighted Arithmetic Mean is computed by using following formula:

${\overline X _w} = \frac{{\sum wx}}{{\sum w}}$
Where:
${\overline X _w}$ Stands for weighted arithmetic mean.
$x$    Stands for values of the items and
$w$   Stands for weight of the item

Example:

A student obtained 40, 50, 60, 80, and 45 marks in the subjects of Math, Statistics, Physics, Chemistry and Biology respectively. Assuming weights 5, 2, 4, 3, and 1 respectively for the above mentioned subjects. Find Weighted Arithmetic Mean per subject.

Solution:

 Subjects Marks Obtained $x$ Weight $w$ $wx$ Math $40$ $5$ $200$ Statistics $50$ $2$ $100$ Physics $60$ $4$ $240$ Chemistry $80$ $3$ $240$ Biology $45$ $1$ $45$ Total $\sum w = 15$ $\sum wx = 825$

Now we will find weighted arithmetic mean as:
${\overline X _w} = \frac{{\sum wx}}{{\sum w}} = \frac{{825}}{{15}} = 55$ marks/subject.