108 LearnersLast updated on June 18th, 2025
Average
An average refers to the mid value of a set of numbers. It can be calculated by adding the given set of numbers and then dividing the sum by the amount of numbers in the set. We will be discussing more about average in this article.
What is Average in Math?
Average is also known as arithmetic mean because it is found by calculating the sum of the values and then dividing it by the number of values. Finding the average is helpful in many scenarios. For instance, it can be used to evaluate the performance of an entire class in a school instead of focusing on individuals.
We can use this formula to calculate the average:
Average = sum of the values/number of values
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How to Calculate Average?
Average is calculated by dividing the sum of the values by the number of values. That means, average = sum of values/number of values.
Sometimes, median can be confused with average. But it is important to understand the difference between them. While average is the mean value of the data, median is the mid value of a dataset arranged in increasing order.
To find the average using the formula, follow these steps:
Step 1: Find the sum of the numbers
Step 2: Finding the number of values
Step 3: Dividing the sum with the total values to find the average
For instance, finding the average of 2, 3, 8, 9, 6, 10.
Step 1: We add the number that is 2 + 3 + 8 + 9 + 6 + 10 = 38
Step 2: Here, the number of values is 6.
Step 3: The average here is 38/6 = 6.333
Applications of Average
Average is applicable in different fields such as statistics and data analysis, science and engineering, and finance and economics. Let’s learn about them in detail.
- Average is used to find the central tendency of the data which is the middle value of the data set.
- To find similarities and make comparisons among data sets.
- To evaluate the performance of an investment, we calculate the average returns
- To find the overall performance of the class and students we calculate the average grade
- It is used to calculate the batting and bowling average in cricket. Batting average is calculated by dividing the total runs scored by the number of dismissals. Bowling average is calculated by dividing the total runs conceded by the total wickets taken.
Tips and Tricks to Master Average
As we know we use average in different fields so it is essential to master average. Let’s learn few tips and tricks to master it
- Understanding the basic concept: That is the average is the ratio of the sum of the values to the number of values.
- Try to memorize the important average formulas, such as:
- The average of first n natural numbers is (n (n + 1)) / 2n = (n + 1)/2
- The average of the square of first n natural numbers = n (n + 1) (2n + 1)) / 6
- The average of the cubes of first n natural numbers = n(n + 1)24
- The average of first n odd numbers = n2
- The average of first n even numbers = n + 1
Common Mistakes and Ways to Avoid Them in Average
In this section let’s learn a few common mistakes which students tend to make when working with average. So that we can avoid them to master average
Mistake 1
Confusing with the types of average
Students usually confuse with different types of average like arithmetic mean, median, mode, average, and so on. So to avoid it students should understand the question and find which is the perfect average for the question.
Mistake 2
Counting the wrong number of values
Students tend to add or omit values while counting the number of values before calculating the average. This will lead to errors, so recheck the number of values to make sure it's correct.
Mistake 3
Rounding too early
Students usually round the value too early, which can reduce the precision. This can be avoided by retaining at least four significant digits throughout the calculation and rounding only at the final step.
Mistake 4
Misreading the word problems
When working on word problems students tend to misread the word problem, that is using the wrong set of numbers or formulas. So students should read the question carefully before working on it.
Mistake 5
Arithmetic errors
Basic calculation errors are common among students. Even simple addition or division can go wrong sometimes. To avoid it, they should recheck the answer and steps to verify whether it is correct or not
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Solved Examples of Average
Problem 1
The marks obtained by a student in five subjects are 78, 82, 91, 76, and 85. Find the average marks.
The average marks = 82.4
Explanation
To find the average marks, we use the formula, average = sum of marks/number of subjects
The sum of the marks = 78 + 82 + 91 + 76 + 85 = 412
Number of students = 5
So, the average = 412 / 5 = 82.4
Problem 2
A worker works 6, 7, 8, 7, and 6 hours over 5 days. Find the average working hours.
The average working hours = 6.8 hours
Explanation
To find the average working hours we use the formula, average = total working hours/number of days
Total working hours = 6 + 7 + 8 + 7 + 6 = 34
Number of days = 5
So, average number of hours worked = 34 / 5 = 6.8 hours
Problem 3
The ages of 5 students are 12, 14, 14, 15, and 16. Find their average age.
The average age = 14.2 years
Explanation
To find the average age we use the formula, average = the sum of the ages/number of students
The sum of the ages = 12 + 14 + 14 + 15 + 16 = 71
Number of students = 5
So, average age = 71 / 5 = 14.2 years
Problem 4
The salaries of five employees in a company are $3000, $3500, $4000, $4500, and $5000. Find the average salary.
The average salary is $4000
Explanation
To find the average salary we use the formula, average = total salary/number of employees
The total salary = 3000 + 3500 + 4000 + 4500 + 5000 = $20000
The number of employees = 5
So, average salary = 20000 / 5 = $4000
Problem 5
The temperature of a city over seven days is recorded as 25°C, 28°C, 30°C, 29°C, 26°C, 27°C, and 31°C. Find the average temperature.
The average temperature is 28°C
Explanation
To find the average temperature we use the formula, average = sum of the temperature/number of days
The sum of the temperature = 25 + 28 + 30 + 29 + 26 + 27 + 31 = 196
So, average temperature = 196 / 7 = 28°C
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FAQs on Average
1.What is average?
2.What is the average formula?
3.Find the average of the first five odd numbers.
4.Find the average of the first five natural numbers.
5.What are the applications of average in daily life
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Jaipreet Kour Wazir
About the Author
Jaipreet Kour Wazir is a data wizard with over 5 years of expertise in simplifying complex data concepts. From crunching numbers to crafting insightful visualizations, she turns raw data into compelling stories. Her journey from analytics to education ref
Fun Fact
: She compares datasets to puzzle games—the more you play with them, the clearer the picture becomes!
