Arithmetic Mean Formula

The sum of all of the numbers in a list, divided by the number of items in that list, is the Arithmetic Mean or Mean of the group. For example, mean of the numbers 5, 7, 9 is 4 because 5 + 7 + 9 = 21 and 21 divided by 3 [there are three numbers] is 7.

Where N is the total number of observations.

Note: Average is not the same as Arithmetic Mean.

Solved Examples

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

Solution:

Example 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

Thus the missing observation is 22.

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