# How to calculate the mean?

• Last Updated : 21 Sep, 2021

Mean is generally the average of a given set of numbers. It is the most important topic in statistics. It is the value that gives the central tendency from a given set of observations. In statistics, there are three measures that define the central values of the observed data they are mean, median, and mode. Mean is usually calculated by dividing the sum of all the numbers and the number of observations in the set. Mean is used for many general purposes like to calculate the average mark of students in all subjects or to calculate the average salary of an employee in a company. There are three different types of means are Arithmetic mean, Harmonic mean, and Geometric mean.

What is the Mean?

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Mean is the central tendency of the distributed data which refers to the average value of the given set of data. Mean corresponds to the single value from the distributed data and represents an appropriate way to explain the data. This is the method most commonly used in statistics to understand and analyze the data. For example, if we want to calculate the average salary of employee present in a company can be calculated by using mean by dividing the sum of all employee salaries and number of employee.

For discrete distribution kind of data, we need to calculate mean by taking the sum of weighted value which is calculated by taking the product of random variable and the probability of random variable.

### How to calculate a mean?

To calculate the mean value we use the mean formula which calculates the average of the given data. It is calculated by dividing the sum of all observed data values to a number of observed values. The mean formula is given by

Mean = (Sum of observed values in data) / (Total number of observed values in data)

There are two steps involved in the calculation of the mean:

Step 1: Calculate the sum of observed values in the data

Step 2: Divide the sum of observed values into the number of observed values in the data

Example: Calculate mean for the following set of data 2, 6, 7, 9, 15, 11, 13, 12?

Solution:

Given,

Observed values 2, 6, 7, 9, 15, 11, 13, 12

Total number of observed values = 8

Since, we know that

Mean = (Sum of observed values in data) / (Total number of observed values in data)

Sum of observed values = 2 + 6 + 7 + 9 + 15 + 11 + 13 + 12 = 75

Total number of oberved values = 8

Mean = 75/8

Mean = 9.375

Therefore, mean for the given observed values = 9.375

### Types of Mean

In statistics the mean is mainly divided into three types they are:

• Arithmetic Mean
• Geometric Mean
• Harmonic Mean

Arithmetic Mean

The arithmetic mean is calculated for a given set of data by calculating the ratio of the sum of all observed values to the total number of observed values.

Arithmetic Mean = (Sum of observed values) / (Number of observed values in data)

Geometric Mean

The geometric mean is calculated for a set of n values by calculating the nth root of the product of all n observed values.

Geometric Mean = nth root of (n1×n2×n3×n4…… n values)

Harmonic Mean

The harmonic mean is calculated by dividing the number of values in the observed set by the sum of reciprocals of each observed data value.

Harmonic Mean = (Number of observed values) / (1/n1 + 1/n2 + 1/n3……….)

### Sample Questions

Question 1: Calculate the mean of the first 5 even numbers?

Solution:

Given,

Observed first 5 even numbers 2, 4, 6, 8, 10.

Total number of observed values = 5

Since, we know that

Mean = (Sum of observed values in data) / (Total number of observed values in data)

Sum of observed values = 2 + 4 + 6 + 8 + 10 = 30

Total number of oberved values = 5

Mean = 30/5

Mean = 6

Therefore, mean for first 5 even numbers = 6

Question 2: Calculate the mean of the first 5 natural numbers?

Solution:

Given,
Observed first 5 even numbers 1, 2, 3, 4, 5.
Total number of observed values = 5
Since, we know that
Mean = (Sum of observed values in data) / (Total number of observed values in data)
Sum of observed values = 1 + 2 + 3 + 4 + 5 = 15
Total number of oberved values = 5
Mean = 15 / 5
Mean = 3
Therefore, mean for first 5 natural numbers = 3

Question 3: Calculate the mean of the first 5 odd numbers?

Solution:

Given,
Observed first 5 even numbers 1, 3, 5, 7, 9.
Total number of observed values = 5
Since, we know that
Mean = (Sum of observed values in data) / (Total number of observed values in data)
Sum of observed values = 1 + 3 + 5 + 7 + 9 = 25
Total number of oberved values = 5
Mean = 25 / 5
Mean = 5
Therefore, mean for first 5 odd numbers = 5

Question 4: Calculate missing values from the observed set 2, 6, 7, x whose mean is 6?

Solution:

Given,
Observed values 2, 6, 7, x
Number of observed values = 4
Mean = 6
Since, we know that
Mean = (Sum of observed values in data) / (Total number of observed values in data)
Sum of observed values = 2 + 6 + 7 + x = 15 + x
Total number of oberved values = 4
6 = (15 + x) / 4
6×4 = 15 + x
x = 9
Therefore, missing value from the set is 9

Question 5: Calculate mean for the following set of data 4, 11, 13, 12?

Solution:

Given,
Observed values 4, 11, 13, 12
Total number of observed values = 4
Since, we know that
Mean = (Sum of observed values in data) / (Total number of observed values in data)
Sum of observed values = 4 + 11 + 13 + 12 = 40
Total number of oberved values = 4
Mean = 40 / 4
Mean = 10
Therefore, mean for the given observed values = 10

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