# Average Formula

The average formula is also known as the arithmetic mean, which is the ratio of the sum of all given observations to the total number of observations. Thus, using the average formula, the arithmetic mean for any sample of data can be calculated. Let's learn about the average formula with a few examples in the end.

## What is the Average Formula?

In this section let's explore the average formula in detail and see its applications through some examples. The average formula for a given set of data or observations can be expressed as:

### Average Formula:

Average = (Sum of Observations) ÷ (Total Numbers of Observations)

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

## Examples Using Average Formula

Let us solve some interesting problems using the Average formula.

**Example 1:** The marks obtained by 8 students in a class test are 12, 15, 16, 18, 20, 10, 11, and 21. Use the average formula and find out what is the average of the marks obtained by the students?

**Solution:**

To find: Average of marks obtained by 8 students

Marks obtained by 8 students in class test = 12, 15, 16, 18, 20, 10, 11, and 21 (given)

Total marks obtained by 8 students in class test =(12+15+16+18+20+10+11+21) = 123/8

Using the average formula,

Average = (Sum of Observation) ÷ (Total numbers of Observations)

Average = (12+15+16+18+20+10+11+21) ÷ 8 = 123/8 = 15.375

**Answer: The average of marks obtained by 8 students is 15.375.**

**Example 2:** The monthly incentives received by an employee for five months are: $21, $27, $31, $19, $22. Using the average formula, calculate the average incentive received by the employee for these five months.

**Solution:**

To find: Average for the given set.

Given:

Incentives for five months(in $): {21, 27, 31, 19, 22}

Using Average Formula,

Average = (Sum of Observation) ÷ (Total numbers of Observations)

Average = (21 + 27 + 31 + 19 + 22) ÷ 5

= 120/5

= 24

**Answer:** Average incentive received by the employee is $24.

**Example 3:** The weight(lb) of students in a class are listed here: {50, 55, 53, 56, 57, 59}. Using the average formula, calculate the average weight of students in the class.

**Solution:**

To find the average weight of students in a class.

Given:

Weights in lb: {50, 55, 53, 56, 57, 59}

Number of students = 6

Using Average Formula,

Average = (Sum of Observations) ÷ (Total number of Observations)

Average = {50 + 55 + 53 + 56 + 57+ 59} ÷ {6} = 330/6 = 55

**Answer: Average weight of students is 55 lb.**

## FAQs on Average Formula

### What is the Average Formula Used For Calculating Average Weight of 9 Students?

The average formula for calculating the average weight of 9 students is expressed as

Average Weight of 9 Students = {Sum of weights of 9 Students} ÷ {Total number of Students}

Average weight of 9 Students = {W1 + W2 + W3 + W4 + .... + W9} ÷ {9}.

### How to Calculate the Average Using Average Formula?

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

### How to Use the Average Formula?

The general average formula is mathematically expressed as Average = {Sum of Observations} ÷ {Total number of Observations}. Let us consider an example to understand its use.

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

Solution: Total number of observations = 6

average = {Sum of Observations} ÷ {Total number of Observations}

Average = (1 + 2 + 3 + 4 + 5 + 6) ÷ 6 = 21/6 = 3.5

Average of (1, 2, 3, 4, 5, 6) is 3.5

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

Average formula for 'n' observations is expressed as

Average of n observations = {Sum of 'n' Observations} ÷ {n}

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