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. For example, the mean of the numbers 5, 7, 9 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 than an Arithmetic Mean.

Solved Examples

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

Solution:

$\overline{x}$ = $\frac{20 + 22 + 24 + 26 + 28 + 30}{6}$
= 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.

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