Arithmetic Mean Calculator

Arithmetic Mean Calculator is a free online tool that displays the mean/average of the given input numbers. BYJU’S online arithmetic mean calculator tool makes the calculations faster and displays the mean value in a fraction of seconds.

How to Use the Arithmetic Mean Calculator?

The mean calculator will provide the central value for the given set of numbers. The procedure to use the arithmetic mean calculator is as follows:

Step 1: Enter the numbers separated by commas in the input field.

Step 2: Click the button “Solve” to get the mean value.

Step 3: The average will be displayed in the output field.

For example, enter the numbers 1, 2, 3, 4, 5 in the mean calculator. Then click the “Solve” button. In a fraction of seconds, the mean calculator will display the mean value as “3” by using the logic:

Mean = Sum of values / Total number of values.

Here, sum of values = 1+2+3+4+5

Total number of values = 5

Hence,  Mean = (1+2+3+4+5)/5 = 15/5 = 3.

What is Arithmetic Mean?

In statistics, one of the most important concepts is an arithmetic mean. The arithmetic mean of the given data can be calculated by adding all the numbers given divided by the total number of values in the set. The arithmetic mean is also called an average. The mean is the commonly used measure of central tendency.

Standard Form

The standard formula to represent the arithmetic mean is as follows:

Arithmetic Mean = (x₁ + x₂ + x₃+….. + x_n ) / n

Where x₁, x₂, x_3, …, x_n are the data values

“n” is the total number of values given

The other form to represent the arithmetic mean is as follows:

Arithmetic Mean = Σ (x_i /n)

How to Calculate Arithmetic Mean?

Example 1: 

Calculate the arithmetic mean for the first 5 multiples of 3.

Solution:

The first 5 multiples of 3 are 3, 6, 9, 12, and 15.

We know that Arithmetic mean = Sum of Observations / Total Number of Observations.

Here, the number of observations is 5.

Hence, Arithmetic mean = (3+6+9+12+15)/5

Mean = 45/5 = 9

Therefore, the mean of the first 5 multiples of 3 is 9.

Example 2: 

Find the mean for the given data set: 5, 7, 12, 10, 23, 25.

Solution:

Given dataset: 5, 7, 12, 10, 23, 25.

Number of observations = 6

Hence. Mean = (5+7+12+10+23+25)/6

Arithmetic mean = 82/6 = 13.66666..

Hence, the mean of 5, 7, 12, 10, 23, 25 is 13.667.