# Arithmetic Mean Formula

Sum of all of the numbers of a group, when divided by the number of items in that list is known as the Arithmetic Mean or Mean of the group.Â For example, the mean of the numbers 5, 7, 9Â is 4 since 5 + 7 + 9 = 21 and 21 divided by 3 [there are three numbers] is 7.
$\LARGE \overline{X}=\frac{\sum_{i=1}^{n}X_{i}}{N}$

Where N is the total number of observations.

Please note that Average is different from an Arithmetic Mean.

### Solved Examples

Q. 1: The marks obtained by 6Â students in a class test are 20, 22, 24, 26, 28, 30. Find the mean.

Solution:

$$\begin{array}{l}\overline{x}\end{array}$$
=
$$\begin{array}{l}\frac{20 + 22 + 24 + 26 + 28 + 30}{6}\end{array}$$

=Â 25
Therefore, mean = 25

Q. 2: If the arithmetic mean of 14 observations 26, 12, 14, 15, x, 17, 9, 11, 18, 16, 28, 20, 22, 8 is 17. Find the missing observation.

Solution:
Given 14 observations are: 26, 12, 14, 15, x, 17, 9, 11, 18, 16, 28, 20, 22, 8
Arithmetic mean = 17
We know that,
Arithmetic mean = Sum of observations/Total number of observations
17 = (216 + x)/14
17 x 14 = 216 + x
216 + x = 238
x = 238 – 216
x = 22

Therefore, the missing observation is 22.