Arithmetic Mean Formula
The arithmetic mean formula calculates the mean or average of the numbers and is used to measure the central tendency of the data. It can be also be defined as the sum of all the given observations to the total number of observations. Let us study the arithmetic mean formula using solved examples.
What is Arithmetic Mean Formula?
To calculate the arithmetic mean of given observations, you just simply add all the given observations and divide the resultant sum by the total number of observations.The arithmetic mean formula to calculate the mean set of observations is given as:
\( \bar{X} = \dfrac{\Sigma_{i = 1}^n X_i}{N} \)
where N is the total number of observations.
Let's take a quick look at a couple of examples to understand the arithmetic mean formula, better.
Solved Examples Using Arithmetic Mean Formula

Example 1: The marks obtained by 8 students in a class test are 10, 19, 12, 21, 18, 20, 11, and19. What is the arithmetic mean of the marks obtained by the students?
Solution:
To find: Arithmetic mean of the marks obtained by the students
Using the arithmetic mean formula,
Arithmetic mean = {Sum of Observation}/{Total numbers of Observations}
Arithmetic mean = (10 + 19 + 12 + 21 + 18 + 20 + 11 + 19)/8= 16.25
Answer: Arithmetic mean of the marks obtained by the students = 16.25.

Example 2: The heights of five students are 164 cm, 134 cm, 155 cm, 156 cm, and,172 cm respectively. Find the mean height of the students.
Solution:
To find: Mean height of the students
Using the arithmetic mean formula,
Arithmetic mean = {Sum of Observation}/{Total numbers of Observations}
Arithmetic mean = (164 + 134 + 155 + 156 + 172)/5= 781/5 = 156.2 cm
Answer: Mean height of the students = 156.2 cm.