# Mean Formula

The mean formula is the average of the numbers and is used to measure the central tendency of the data. The mean formula can also be defined as the sum of all observations to the total number of observations. In this section, we will learn more about the mean formula and how to apply it.

## What Is the Mean Formula?

The mean formula is defined as the sum of the observations divided by the total number of observations. The formula to calculate the mean will be helpful in solving a majority of the topics related to the mean.

### Mean Formula:

The mean formula of given observations can be expressed as,

Mean Formula = (Sum of Observations) ÷ (Total Numbers of Observations)

Hence, the average of all the data points is termed as mean.

## Examples on Mean Formula

Let us solve some interesting problems using the mean formula.

**Example 1: **The marks obtained by 8 students in a class test are 12, 14, 16, 18, 20, 10, 11, and19. Use the mean formula and find out what is the mean of the marks obtained by the students?

**Solution: **

To find: Mean of marks obtained by 8 students

Marks obtained by 8 students in class test = 12, 14, 16, 18, 20, 10, 11, and19 (given)

Total marks obtained by 8 students in class test =(12+14+16+18+20+10+11+19) =120

Using the mean formula,

Mean = (Sum of Observation) ÷ (Total numbers of Observations) = 120/8 = 15

**Answer: The mean of marks obtained by 8 students is 15.**

**Example 2: T**he heights of five students are 161 in, 130 in, 145 in, 156 in, and,162 in respectively. Find the mean height of the students.

**Solution:** To find: the mean height of the students.

The heights of five students = 161 in, 130 in, 145 in, 156 in, and,162 in (given)

Sum of the heights of five students =(161+130+145+156+162) = 754

Using Mean Formula,

Mean = {Sum of Observation} ÷ {Total numbers of Observations}= 754/5=150.8

**Answer: The mean height of the students is 150.8 inches.**

**Example 3: **Find the mean of the first five natural odd numbers, using the mean formula.

**Solution: **

The first five natural odd numbers = 1, 3, 5, 7, and 9

Using mean formula

Mean = {Sum of Observation} ÷ {Total numbers of Observations}

Mean = (1 + 3 + 5 + 7 + 9) ÷ 5 = 25/5 = 5

**Answer: The mean of the first five natural odd numbers {1, 3, 5, 7, 9} is 5.**

## FAQs on Mean Formula

### What Is the Difference Between Mean Formula and Median Formula?

The mean formula is given as the average of all the observations. It is expressed as Mean = {Sum of Observation} ÷ {Total numbers of Observations}. Whereas, the median formula is totally dependent on the number of observations (n). If the number of observation is even then the median formula is [Median = ((n/2)^{th} term + ((n/2) + 1)^{th }term)/2] and if n = odd then the median formula is [Median = {(n + 1)/2} ^{th }term].

### How To Calculate the Mean Using Mean Formula?

If the set of 'n' number of observations is given then the mean can be easily calculated by using a general mean formula that is, Mean = {Sum of Observation} ÷ {Total numbers of Observations}.

### How To Use the Mean Formula?

The general mean formula is mathematically expressed as Mean = {Sum of Observation} ÷ {Total numbers of Observations}. Let us consider an example to understand its use.

Example: Find the mean of (1, 2, 3, 4, 5, 6, 7)

Solution: Total number of observation = 7

Mean = {Sum of Observation} ÷ {Total numbers of Observations}

Mean = (1 + 2 + 3 + 4 + 5 + 6 + 7) ÷ 7 = 28/7 = 4

Mean of (1, 2, 3, 4, 5, 6, 7) is 4

### What Will Be the Mean Formula for n Observations?

Mean formula for 'n' observations is expressed as

Mean of n observations = {Sum of 'n' Observation} ÷ {Total numbers of 'n' Observations}