[Maths Class Notes] on Difference Between Mean and Average Pdf for Exam

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 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