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Difference Between Mean and Average

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Last updated date: 29th May 2024
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Learn the Difference Between Average and Mean


Mathematics as a subject is not limited to numbers and counting. The scope of the subject is enormous. It has significant usage in other fields like physics, economics, accounting, and so on. In this article, we will discuss one such important topic related to Mean and Average. 


If you observe your day-to-live you will come to analyze the frequent usage of the concept mean and average. To strengthen the conceptual clarity of the students and to help them score good marks in the exams, a team of experts at Vedantu has explained the concepts in the best possible manner. 


Students need to download and refer to the free PDF and the video lectures to boost their level of preparation. 


Average and Mean

Average and mean are the two terms which are often used interchangeably. 

 

The average is calculated for those sets of values which are more or less the same, i.e. the difference between them is very less. While mean is calculated for those sets of values having more difference or close to each other.

 

However in Statistics, the term “Mean” is used in place of the term “Average”.

 

What is Average? 

The average is defined as the sum of given numbers divided by the total number of numbers being averaged.

 

Mathematically, \[\text{Average} = \frac{\text{Sum of given number}}{\text{Total number of number}}\]

 

An average is a single number taken as representative of a list of numbers. Often, Average refers to the arithmetic mean.

 

Let’s understand it by an example

Given a set of numbers: 2, 3, 5, 8 and 10.

Sum of given numbers = 2 + 3 + 7 + 8 + 10 = 30.

Total number of numbers in given set = 5.

So, \[\text{Average} = \frac{30}{5} = 6\] 

 

What is Mean?

Mean is the central point of the set of values. It is the average of values present in the data set. The central value which is called the average in mathematics is called the mean in statistics.

 

Usually, Mean refers to the arithmetic mean but it can take other forms like Harmonic Mean, Geometric Mean, etc. these forms of mean are used in different situations based on the distribution and nature of data.

 

It can also be defined as the sum of the smallest value and the largest value in the given data set divided by 2.

 

Mathematically, \[\text{Mean} = \frac{\text{Sum of smallest and largest value of data set}}{2} \]


So, from the previous example


Smallest number = 2, Largest number = 10.


\[\text{Mean} = \frac{2 + 10}{6} = 6\].


Therefore, we can say that average is mean but the reverse is not true.


Types of Mean 

Mean are classified into three types - 

  1. Arithmetic Mean

  2. Geometric Mean

  3. Harmonic Mean


Arithmetic Mean: It is the sum of values of the given set divided by the total number of values of the set.


Geometric Mean: It is similar to the arithmetic mean but instead of adding we multiply the numbers and take the square root in case of 2 numbers, cube root in case of 3 numbers and so on.


Harmonic Mean: It is reciprocal of the arithmetic mean.


Difference Between Average and Mean


S.No.

Average

Mean

1.

It is the sum of the numbers divided by how many numbers are being averaged.

It is the sum of the smallest value and the largest value in the given data set divided by 2. 

2.

Average refers to the arithmetic mean.

There are 3 different types of mean.

3.

Average is calculated for those sets of values which are more or less the same.

Mean is calculated for those sets of values which have more difference or they are not at all close to each other.

4.

An average is a single number taken as representative of a list of numbers.

Mean is the central point of the set of values

5.

Average is usually used in casual English conversation.

Mean is usually used in technical language, in statistics, or data interpretation. 


FAQs on Difference Between Mean and Average

1. What is the average of the first ten (10) natural numbers? 

Students first need to know what is natural. All the numbers from 1 to infinite are natural numbers. We have explained the concept in detail in the chapter Number system.  So, the 10 natural numbers are 1,2,3,4,5,,6,7,8,9,and 10. 


\[\text{Average} =  \frac{\text{Sum of given number}}{\text{Total number of number}}\]


      = \[\frac{1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10}{10}\]

      = \[\frac{55}{10}\]

      = 5.5 


The process of finding the average is very simple, just remember the basic concept. Try finding the average of your marks scored in your term exams. 


Practice the questions from the available set of sample question papers and solutions. 

2. Why mean is more in use instead of the average? 

Average is used more in general, when might not get the central tendency with the help of average. So, in order to find the central tendency of any given set of data we make the use of Mean. 


In other words, it helps you reach the central point of the data set. 


The concepts have been explained in detail on the website of the Vedantu. These study materials help you understand the use and application of the concepts in the real-life scenario. 

3. How can I get comfortable with the problems of mean and average?

Mathematics is all about practice, the more you practice the better you get with solving the related problems. 


In order to be a master in solving the topics of Mean and Average, students first need to cover the topic from the textbooks or the free PDF available on the website of the Vedantu. A student can also refer to the video lectures related to the topic prepared by the faculty of Vedantu. 


After understanding the concept, start practicing the questions of the textbooks. Solutions and sample papers of every topic are made available on the website. 


If a student regularly practices the process they can excel in any given topic. 

4. Is the topic Mean and average important for other competitive exams? 

Topics like mean and average form the fundamental base for other subjects and topics of math, economics, and statistics. In various competitive exams like IIT JEE, UPSC, SSC, IBPS, a large number of questions appear from the topic mean and average.


Students cannot skip the topic at any cost. Try to solve as many questions related to the concept according to the demand of the paper. The chapter is not only interesting but also very simple and can increase your exam scores to a great extent.