# Average

## What is Meant by Average or Definition of Average?

• The mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set is known as average.

• Average has many applications both in real-life.

•  Suppose if we need to find the average age of men or women in a village or average female height in India, then we can calculate it by adding all the values and dividing it by the number of values we have added.

• Here’s the average formula in maths that evaluates the average of the given set of numbers:

Average formula in maths  = $\frac{ Sum \; of \; the \; terms }{ Total \; number \; of \; terms }$

### Average Symbol:

• The average can basically be defined as the mean of the values which are represented by x̄ (x bar) also known as the average symbol.

• The average symbol can be denoted by ‘μ’.

### Average Formula in Maths:

The formula that will tell you how to calculate the average of a list of numbers or values is very simple in Mathematics.

Here are the steps that will tell you how to calculate the average:

Step 1) Firstly, you need to add all the numbers given in the list

Step 2) Then divide the calculated sum by the number of terms given in the list.

Step 3) The average of numbers can be expressed as:

Average = Sum of Values of the list/ Total Number of values in the list

Here’s an average example for better understanding,

Given a set of values: 1, 2, 3, 4, and 5.

We know that Average = Sum of all the values of the list / total number of values in the list.

Step 1) Sum of the numbers (1+2+3+4+5) = 15

Step 2) Total number of terms = 5, divide the sum by the total number of terms,

Putting the sum and the number of terms in the formula that we know from the definition of average,

Average = Sum of Values of the list/ Total Number of values in a list

Average = 15/5 = 3

### What is the Average of Negative Numbers?

If there are negative numbers present in the list of numbers, even then the process or formula to calculate the average remains the same.

Average of negative numbers =  $\frac{ Sum \; of \; the \; terms }{ Total \; number \; of \; terms }$

Let’s understand the concept of an average of negative numbers with an example:

Average examples: Find the average of 4, −7, 5, 10, −1.

Solution) Lets’ first find the sum of the given numbers,

= 4 + (-7) + 5 + 10 + (-1)

= 4– 7 + 5 + 10 – 1

= 11

Total number of terms = 5

As we know the formula to calculate the average from the definition of average,

Average = $\frac{ Sum \; of \; the \; terms }{ Total \; number \; of \; terms }$

Average = $\frac{6}{5}$

Average is equal to 1.2.

### What is the Difference Between Mean and Average?

Here’s the main difference between mean and average,

## Difference Between Mean and Average

 Average can be defined as the sum of values divided by the total number of terms. Whereas, mean can be defined as the sum of the largest and the smallest number in the list divided by 2.

### Questions to Be Solved (Average Examples):

Question 1) Find the average of the first five even numbers.

Solution) In Mathematics, the first five even numbers are as follows: 2, 4, 6, 8, 10

Now we will add these numbers = 2 + 4 + 6 + 8 + 10 = 30

Total number of terms = 5

As we know the formula to calculate the average,

Average = $\frac{ Sum \; of \; the \; terms }{ Total \; number \; of \; terms }$

Average = $\frac{30}{5}$

The average is equal to 6.

Question 2) Find the average of the given numbers 6, 13, 17, 21, 23.

Solution) Let’s add the given numbers =

= 6 + 13 + 17 + 21 + 23 is equal to 80

Total number of terms = 5

As we know the formula to calculate the average,

Average = $\frac{ Sum \; of \; the \; terms }{ Total \; number \; of \; terms }$

Average = $\frac{80}{5}$

The average is equal to 16.

Question 3) If the age of 10 students in a football team is 12, 13, 11, 12, 13, 12, 11, 12, 12, 2. Then find the average age of the students in the football team.

Solution) Given, the age of students are 12, 13, 11, 12, 13, 12, 11, 12, 12 , 2.

Let’s find the sum of the ages of students,

Sum = (12+13+11+12+13+12+11+12+12+2) = 120

Total number of terms = 10

As we know the formula to calculate the average,

Average = $\frac{ Sum \; of \; the \; age \; of \; the \; students \; of \; the \; football \; team }{ Total \; number \; of \; students}$

Average = $\frac{120}{10}$

The average age of the students of the football team is equal to 12.

Question 4) If the heights of females in a class are 5.5, 5.3, 5.7, 4.9, 6, 5.1, 5.8, 5.6, 5.4, and  6. Then find the average height of females of the class.

Solution) Given the height of females= 5.5, 5.3, 5.7, 5.9, 6, 5.1, 5.8, 5.6, 5.4, 6

Sum = (5.5+5.3+5.7+4.9+6+5.1+5.8+5.6+5.4+6)

Total number of terms = 10

As we know the formula to calculate the average,

Average = $\frac{ Sum \; of \; the \; heights \; of \; females }{ Total \; number \; of \; females}$

Average = $\frac{55.3}{10}$

The average height of the females in the class is 5.3.

1. How Do I Calculate the Average and Why is Average Important?

The average of a set of numbers can be calculated by finding the sum of the numbers divided by the total number of values (n) in the set. For example, suppose we want to find the average of 1, 5, 4, 7, and 13. We simply find the sum of the numbers: 1+5+4+7+13 = 30 and as there are five numbers, when we divide 30 by 5 to get 6. Average can be easily calculated using the average calculator.

Average is important because -

1. Average helps us to summarize a large amount of data into a single value.

2. Average indicates some variability around any single value within the original data.

2. Why Do We Calculate the Average and What Do You Mean By Average?

The term average is generally used frequently in everyday life to express an amount that is typical for a group of people or a group of things. Averages are useful because they:

• They summarize a large amount of data into a single value.

• Average indicates that there is some variability around this single value within the original data.

Average can be easily calculated using the average calculator.

We can easily calculate the average using the average calculator. The result that we get when we add two or more numbers together and divide the sum by the total number of terms is known as average. Average example, suppose if we want to find the average of 1, 6, 3, and 2. We simply find the sum of the numbers: 1+6+3+2= 12 and as there are four numbers (n=4), when we divide 12 by 4 we get 3.