Average and Mean, both have their significance in mathematics. Average and mean are considered to be similar but they have different meanings associated with them. There are different situations in our day-to-day lives, where we use the terms 'mean' and 'average' interchangeably.
We use the word "Average" for any situation where we have to give a lump sum or approximate idea of a value. However, the word "Mean" is specifically used in the context of data in statistics. Both Average and Mean can be calculated by taking the sum of the given data and then dividing it by the total number of data.
In this article, we will explain both the terms mean and average and the difference between mean and average followed by solved problems on mean and average. At the end of the article, we will have some practice problems and FAQs related to mean and average.
What is Average?
Average is defined as the term referring to the sum of terms on which we need to perform average divided by the total count of the number of terms.
Average can also be termed as the arithmetic mean in mathematics as it represents a collective value for the given terms in the range. The word average can be used in any domain of science and engineering as well as in our daily lives. In daily life, we calculate what is the average temperature for the week or for the month. We use the term average strike rate for a batsman and average economy rate for a bowler. Hence, we see that the word, average is very generic and is used in almost every domain.
The formula for calculating average is discussed below:
The formula for average is given as:
Average = ( Sum of terms)/ (Total count of terms)
Average Example
Example: The run scored by a batsman in 5 matches are 20, 31, 52, 45, 97. Find his average strike rate.
Solution:
Average Strike Rate = (20 + 31 + 52 + 45 + 97)/5 = 245/5 = 49
Hence, on an average the batsman scored 49 runs per over.
What is Mean?
Mean is defined as the term referring to the the middle value of the given dataset of which we need to find mean.
Mean is used to find the central tendency of the dataset. The term mean is specifically used in the field of statistics. We can also say that Mean is the average of the given dataset. Mean can be found by dividing the sum of given terms by total number of terms. Another way of finding mean for a continuous data is adding the greatest and smallest term of the progression and then dividing it by 2. Mean is of different types namely, Arithmetic Mean, Geometric Mean, Harmonic Mean and Weighted Mean. Mean formula is given for both grouped and ungrouped data.
Let's see the Mean Formula
The formula of Mean is given as:
Mean(\bar X
) = (x1 + x2 + x3 + .... + xn)/n
Mean is also calculated as (smallest term + largest term)/2. However this is only valid for an arithmetic progression. Mean can also be calculated for grouped data by Mean for Grouped Data Formula. Let's learn an example of mean
Mean Example
Example: Find the mean age of students if the individual age of students are 11 years, 13 years, 12 years, 11 years and 15 years.
Solution:
Mean Age = (11 + 13 + 12 + 11 + 15)/5 = (62)/5 = 12.4 years
Is Average and Mean the Same?
Mathematically, Average and Mean are same. The basic formulas used to calculate average and mean are also the same. We can even say that average is the mean of the given data and mean is the average of the given dataset. However, the difference between them lies in context in which they are used.
The term Average is used to estimate an approximate value of a given data in general purpose, it may be weight of students of a class, number of cars crossing a traffic signal, water intake by a person or maybe similar things. However, the use of word in "Mean" is specifically used in the context of statistics. Mean is specifically used to represent the average of the statistical data which may be share price variation of a company, population statistics of a country, agriculture production data etc. Mean is of the tool to find the central tendency of the given dataset.
Average vs Mean
Average and Mean are often used interchangeably but are different in meaning. Listed below are the differences between average and mean:
Average | Mean |
|---|
Average is defined as sum of terms on which we need to perform average divided by the total count of the number of terms. | Mean is the smallest term of all the given terms summed up with the largest term and then the result is divided by 2. as well as dividing sum of terms by total number of terms |
Average is recommended for calculation for terms that are close to each other. | Mean is recommended for calculation for terms that differ from each other and are not closely related. |
Average refers to be arithmetic mean of a given value set. | Mean can be referred for arithmetic, geometric or harmonic mean of a given value set. |
Here, the denominator is the collective sum of all the given terms for which we need to calculate average. | Here, the denominator is 2 or number of terms i.e. n based of the types of dataset given. |
Also, Check
Solved Examples on Average & Mean
Example 1. Calculate the mean of given terms: 5, 28, 30, 8, 2, 10.
Solution:
Mean = (5 + 28 + 30 + 8 + 2 + 10)/6
⇒ Mean = 63/6 = 13.83
Example 2. Calculate the average of given terms: 10, 20, 30, 40.
Solution:
Sum of all the terms = 10 + 20 + 30 + 40
Sum of all the terms = 100
Total number of terms = 4
Average = (Sum of all the terms) / ( Total number of terms )
= 100/4
=25
Example 3. Calculate the mean of given terms: 10, 20, 30, 40, 50
Solution:
Smallest number of given terms is 10 and largest number in the given terms is 50.
Note here that the terms are in Arithmetic Progression, hence we will use the following formula:
Mean = (smallest term + greatest term )/2
= ( 10 + 50 ) /2
= 30
Note: The result from the above formula and conventional formula will be same.
Example 4. Calculate the average of given terms: 5, 2, 3, 7, 9, 4
Solution:
Sum of all the terms = 5 + 2 + 3 + 7 + 9 + 3
Sum of all the terms = 29
Total number of terms = 6
Average = (Sum of all the terms) / ( Total number of terms )
= 29/6
Example 5. Calculate the mean of given terms: 5, 8, 3, 7, 2, 1.
Solution:
Mean = (5 + 8 + 3 + 7 + 2 + 1)/6
= ( 26 ) /6
= 4.33
Practice Problems on Average & Mean
Q1. Find mean of the following terms: 10, 4, 6, 12, 14.
Q2. Find average of following terms: 2, 4, 6, 8.
Q3. Find mean of the following terms: 13, 17, 18, 11, 19.
Q4. Find mean of the following terms: 4, 6, 12, 14, 7, 5, 2
Q5. Find average of following terms: 3, 4, 6, 2, 7.
Conclusion
Average and mean is crucial for both general applications and statistical analysis. While these terms are often used interchangeably, they serve distinct purposes in different contexts. The average provides a general estimation and is widely used in everyday scenarios, from calculating temperatures to sports statistics. On the other hand, the mean specifically addresses the central tendency within a dataset and is a fundamental concept in statistics, and have various types such as arithmetic, geometric, and harmonic means.
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