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 same, i.e. the difference between them is very less. While mean is calculated for those set of values having more difference or close to each other.
However in Statistics, the term “Mean” is used in place of the term “Average”.
The average is defined as the sum of given numbers divided by the total number of numbers being averaged.
Mathematically, Average = \[\frac{{Sum{\text{ }}of{\text{ }}given{\text{ }}number}}{{{\text{Total number of number}}}}\]
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, Average = \[\frac{{30}}{5}\]= 6.
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 as average in mathematics is called as 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, Mean = \[\frac{{{\text{Sum of smallest and largest value of data set }}}}{2}\]
So, from the previous example
Smallest number = 2, Largest number = 10.
Mean = \[\frac{{2 + 10}}{6}\]= 6.
Therefore, we can say that average is mean but the reverse is not true.
Arithmetic Mean
Geometric Mean
Harmonic Mean
It is the sum of values of the given set divided by the total number of values of the set.
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.
It is reciprocal of the arithmetic mean.
Key points of average and mean are summarised in the following table.
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 set of values which are more or less the same. | Mean is calculated for those set 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. |
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