Mean Rugby Scores

Warm-up:

Calculating the Mean
(care of thirdspacelearning.com)

The Problem:

A rugby team has a mean score of 10.5 after eight games. The next game increases the mean to eleven.

What was the score in that game?

-/|\-

Solution:

So, we are told that after eight games the mean is 10.5, i.e.,

$$10.5=\frac{S}{8}$$

where $S$ is the sum of all the scores and is

$$S=84$$

The ninth game adds an unknown amount to this, $84+x$, therefore the new mean

$$11=\frac{84+x}{9}$$

So, $x=15$ the score of the ninth game.

Further Reading:

Averages
(care of revisionmaths.com)

Measures of location and spread
(care of mathswithdavid.com)