# Average: Definition of Average, Average Symbol and Average Formula in Math՚S (For CBSE, ICSE, IAS, NET, NRA 2022)

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An **average** of a list of data is the expression of the central value of a set of data. Mathematically, it is defined as the ratio of summation of all the data to the number of units present in the list. For example, the average of is . So, 3 is the central value of 2,3 and 4. It is also termed as mean of the given values in statistics. Learn to calculate average value here.

## Definition of Average

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

The average formula has many applications both in real-life. Suppose if we have to find the average age of men or women in a group or average male height in India, then we calculate it by adding all the values and dividing it by the number of values.

Average can be calculated as:

## Average Symbol

The average is basically mean of the values which are represented by . It is also denoted by the symbol .

## Average Formula in Math՚S

The formula to find the average of given numbers or values is very easy. We just have to add all the numbers and then divide the result by the number of values given. It can be expressed as:

Suppose, we have given with number of values such as The average or the mean of the given data will be equal to:

The Arithmetic mean is the most common type of Average. If n numbers are given, each number denoted by (where ) , the arithmetic mean is the sum of the as divided by n, then:

where,

- is the number of observations
- represent index of summation
- and data value for the given index

## How to Calculate Average?

We can easily calculate the average for a given set of values. We just have to add all the values and divide the outcome by the number of given values. Let us understand with an example.

If there are a group of numbers say . Then find the average of these values.

By average formula, we know,

Here sum of value

No. of observation

Sum of the value.

Hence, the average of given values is 11.42

## Average of Negative Numbers

If there are negative numbers present in the list, then also the process or formula to find out the average is the same. let՚s understand this with an example.

**Example: Find the average of 5, − 9,8, 15, − 3**

**Solution**:

Here given some numbers,

Formula for finding average is

Here no. of observation

First, we sum of the values but here given some negative value and some positive value so, we do the sum of positive value and sum of negative value.

Sum of positive value , Sum of negative value

Here one is positive, and one is negative the operation is subtraction, and put the sign of greater value.

- Hence, the average of this value is 3.2.
- How does this whole idea of average or mean works? Average helps you to calculate on how to make all the units present in a list equal.

## Average Examples

**1) Find the average of 12, 14,16, 18**.

**Solution**:

Here sum numbers are given,

- For average
- No. of observation is 4.

First sum of the values,

Then sum of the value divided by the no. of observation,

Hence, we get the average of given numbers.

**2) Find the average of 8, 15, 19,23, 27**

**Solution**:

Here sum numbers are given,

- For average
- No. of observation is 5.

First sum of the values,

Then sum of the value divided by the no. of observation,

Hence, we get the average of given numbers.

**3) If the age of 9 students in a team is 22, 23, 21, 22, 23, 22, 21,22, 22. Then find the average age of students in the team**.

Solution:

- Here given the age of 9 students.
- The ages are 22, 23, 21, 22, 23, 22, 21,22, 22.
- We have to find out average.
- Formula for Average,

Here no. of students is 9.

First find the sum ages.

For the find of average, sum of ages divided by the no. of students.

Hence, the average age of students in a team is 12 years.

**4) If the heights of males in a group are 5.2,5.4,5.6,5.8,6, 5.9,5.7,5.5,5.3,6. Then find the average height**.

Solution:

Here given the heights of male in a group are 5.2,5.4,5.6,5.8,6, 5.9,5.7,5.5,5.3,6.

- We have to find out average.
- Formula for Average,

Here no. of male is 10.

First find the sum heights.

For the find of average, sum of heights divided by the no. of male.

Hence, the average height of male is 5.6 years.