### Theory:

The arithmetic mean is a fancy term for the average. The simplest formula for mean or average adds up the numbers you want to average and divided by the number of items.

To write a simple mathematical expression for arithmetic mean or average or mean is,

$\mathit{Arithmetic}\phantom{\rule{0.147em}{0ex}}\mathit{mean}\phantom{\rule{0.147em}{0ex}}=\frac{\sum _{n\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}1}^{k}{X}_{n}}{k}\phantom{\rule{0.147em}{0ex}}$

The sum of $$k$$ different numbers divided by $$k$$.
Example:
A batsman scored the following number of runs in six innings:
$$36, 35, 50, 46, 60, 55$$
Calculate the mean runs scored by him in an inning.

Solution:
Total runs $$= 36 + 35 + 50 + 46 + 60 + 55 = 282$$.
To find the mean, we do the sum of all the observations and divide it by the number of observations.
Therefore, in this case, mean $$=$$ $\frac{282}{6}$ $$= 47$$.
Thus, the mean runs scored in an inning is $$47$$.