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# Average in Maths (Definition, Symbol, Formula & Examples)

## Average Introduction

Averages are used to represent the central tendency of a set of data. They provide a summary of the data by indicating the typical value around which the data cluster. Averages, also known as the mean or Arithmetic Mean. In this article, we will discuss the concept of averages, the different types of averages, and How to Calculate Average?

## Average Definition

An average is a measure that summarizes a set of data by indicating the central tendency or typical value of that set. It is also known as a measure of central tendency. There are three commonly used types of averages, which are mean, median, and mode.

## Types of Averages

1. Mean: The mean is the most commonly used average. It is the sum of all the values in a set of data divided by the total number of values. The formula for calculating the mean is:

Mean = Sum of all values / Number of values

1. Median: The median is the middle value of a set of data. It is the value that separates the data into two equal halves.
2. Mode: The mode is the value that occurs most frequently in a set of data. If there is more than one mode, the set is said to be bimodal, and if all values occur equally, the set has no mode.

### Average Formula

The average formula refers to the mathematical formula used to calculate the central tendency of a set of numerical data.

Average = (Sum of all values) / (Number of values)

## How to Calculate Average?

Here are the steps to calculate the Average of a data set:

Step 1: Add up all the values in the data set.

Step 2: Count the total number of values in the data set.

Step 3: Divide the sum of all the values by the total number of values.

Average = (Sum of all values) / (Number of values)

For example, to calculate the mean of the numbers 2, 4, 6, 8, and 10:

Step 1: 2 + 4 + 6 + 8 + 10 = 30

Step 2: There are 5 values in the data set.

Step 3: Mean = 30 / 5 = 6

Therefore, the mean of the numbers 2, 4, 6, 8, and 10 is 6.

### Solved Examples on Averages

Example 1: The marks obtained by 6 students in a test are 78, 84, 67, 91, 76 and 82. Find the average marks.

Solution: To find the average, we add up all the marks and divide by the total number of students:

Average marks = (78 + 84 + 67 + 91 + 76 + 82) / 6 = 478 / 6 = 79.67

Therefore, the average marks obtained by the 6 students is 79.67.

##### Example 2: The monthly salaries of a group of 8 employees are: $2500,$3100, $2900,$3400, $3200,$2700, $2800, and$3000. What is the average monthly salary?

Solution: To find the average, we add up all the salaries and divide by the total number of employees:

Average salary = ($2500 +$3100 + $2900 +$3400 + $3200 +$2700 + $2800 +$3000) / 8 = $24,800 / 8 =$3100

Therefore, the average monthly salary of the 8 employees is $3100. Example 3: A car travels 240 km in 4 hours. What is the average speed of the car in km/h? Solution: To find the average speed, we divide the total distance traveled by the time taken: Average speed = 240 km / 4 hours = 60 km/h Therefore, the average speed of the car is 60 km/h. ##### Example 4: The price of 5 different books are$12, $18,$20, $15 and$25. What is the average price of the books?

Solution: To find the average price, we add up all the prices and divide by the total number of books:

Average price = ($12 +$18 + $20 +$15 + $25) / 5 =$90 / 5 = $18 Therefore, the average price of the 5 books is$18.

## Frequently Asked Questions on Averages

What is an average?

An average is a measure of central tendency that represents a typical value of a set of data. It is also known as the mean and is calculated by adding up all the values in a set of data and dividing by the total number of values.

What are the different types of averages?

There are three types of averages: mean, median, and mode.

##### What is weighted average?

A weighted average is an average that takes into account the relative importance or weight of each value in a set of data. Each value is multiplied by its weight and then the sum of the products is divided by the sum of the weights.

How is the average useful?

The average is useful in summarizing a set of data by giving a typical value that represents the central tendency of the data. It helps in comparing different data sets and in making decisions based on the data.

What is the difference between mean and median?

Mean is the sum of all values in a set of data divided by the total number of values, while median is the middle value in a set of data when it is arranged in order. Mean is affected by outliers, while median is not.

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