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**Average Formula**: One of the most often-used mathematical formulas is the average formula, particularly in the context of quantitative operations. In mathematics, an average is a number figure that is used to represent a huge amount of data. As a result, the average value is used since it helps to express all of the values in a single value.

## Average Definition

“average is to determine the mean or center value of a set of data”

The average is easily estimated by adding all of the data values and dividing them by the number of elements. In this article, we are going to learn about the Average Formula, and how to calculate the average along with solved examples in this post.

## What is Average?

In mathematics, an average of a set of data is the expression of the set’s center value. It is defined mathematically as the ratio of the sum of all the data to the number of units in the list. The average value of a group of integers is the computed “central” value in mathematics. The middle or ‘center’ point is referred to as the ‘average’. Understanding averages helps us handle vast volumes of data more effectively and has many practical uses.

## Average Formula in Maths

The definition of average is to determine the mean or center value of a set of data.The average Formula is widely used to determine the center value. It is fairly simple to calculate the average of a set of numbers or values using the average formula. By adding up all the data values and dividing them by the total number of items, it is simple to determine the average. As a result, the following is the mathematic average formula:

**Average formula = Sum of Values/ Number of values**

Suppose, we have given with n number of values such as x_{1}, x_{2}, x_{3} ,….., x_{n}. The average or the mean of the given data will be equal to:

**Average = (x _{1}+x_{2}+x_{3}+…+x_{n})/n**

For Example, The average of 5, 10, 12. 18. and 35 is (5+10+12+18+35)/5= 80/5 = 16. As a result, the average of the given number set is 16.

## How to Calculate Average with the formula?

Using the Average formula we can easily find out the mean or central value for a given set of variables is simple to compute. We only need to follow the steps below when computing the Average.

Step 1: The first step in calculating the average of numbers is to add all of the given numbers together.

Step 2: Next, we must count the number of numbers in the given dataset.

Step 3: Utilize the Average formula to determine the outcome. Divide the sum by the number of observations to get the average. The formula for calculating the average of a number is:

Average = Sum of the Observations / Number of Observations.

## Arithmetic mean Symbol

The arithmetic mean is also known as the mean or arithmetic average. It is calculated by summing all of the numbers in a given data set and then dividing the total number of items in that set by the total number of items in that set. The arithmetic mean is nothing but the ratio of the total number of observations to the sum of all provided observations.

For Example, A given number set with n integers, each symbolized by ai (where i = 1,2,…, n), the arithmetic mean is the total of the as divided by n, then:

## Averages Formula

Averges-based problems appear frequently in both Board Exams and Competitive Exams. Students can use the following average formulas to answer problems about averages:

Average Formulas List | |

Average formula of first n natural numbers | (n+1) / 2 |

Average of first n even numbers | n + 1 |

Average of first n odd numbers | n |

Average of squares of first n even numbers | (n+1) (2n+1) / 6 |

Average of squares of first n natural numbers | n (n+1)2 / 4 |

Average of squares of first n odd numbers | (2n+1) (2n-1) / 3 |

Average of cube of first n even numbers | 2n (n+1)2 |

Average of cube of first n odd numbers | n(2n²– 1) |

Average of cubes of first n natural numbers | n (n+1)2 / 4 |

Average Formula Examples

**Example 1: Calculate the average of 10, 13, 22,45, and 60. **

Solution: Sum of the all given numbers = 10+ 13 + 22 + 45 + 60 = 150

In the given Number set there, a is a total of 5 no present.

**Average formula = Sum of Values/ Number of values**

The Average of the Given Number set is = 150/5 = 30

**Example 2:** If the weights of the 7 students in a group are 42, 50, 38, 36,47,44, 37. Then, determine the average weight of the students in that group

Solution:

The students’ ages are 42, 50, 38, 36,47,44, and 37.

**Using the Average formula we can say that, Average = Sum of Values/ Number of Students.**

In the given problem, the Sum of 7 students’ wright is (42+50+38+36+47+44+37)=294

Total number of members in this Group =7

Average = 294/7= 42.

As a result, the average weight of students in the group is 42 years.