# How do you find the average of the percentages ?

Last updated date: 29th Mar 2023

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**Hint**: In the given question, we are asked to find out how we are supposed to find the average or the mean of the percentages given to us. Percentage is a number or ratio that represents a fraction with \[100\] as the denominator. It is usually denoted by the symbol ‘%’ and is also referred to as “percent” or “pct”. Finding the mean or average of percentages is an easy task and can be determined easily.

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__Complete step-by-step answer__So, we have to evaluate the average or mean of the percentages. Hence, we first see how to calculate the average of simple numbers and then proceed to percentages.

The mean is the average of numbers. It is easy to calculate. First adding up all the observations or numbers and then dividing by the number of observations.

The mean of percentages can also be calculated in a similar way.

So, let us assume that there are three percentages given to us: $ p\% $ , $ q\% $ and $ r\% $ .

Now, we calculate the mean by adding up all the percentages and then dividing by the number of percentages.

So, Mean $ = \left( {\dfrac{{p\% + q\% + r\% }}{3}} \right) $

Hence, this way we calculate the mean of percentages.

Let’s take an example to understand it more clearly. The three percentages p, q and r be $ 15\% $ , $ 35\% $ and $ 70\% $ . Then, to find the average of these percentages $ 15\% $ , $ 35\% $ and $ 70\% $ , we follow the method described above. So, we get,

Average of the percentages $ = \left( {\dfrac{{70\% + 35\% + 15\% }}{3}} \right) $

$ \Rightarrow \left( {\dfrac{{120\% }}{3}} \right) $

$ \Rightarrow 40\% $

So, the mean of the percentages $ 15\% $ , $ 35\% $ and $ 70\% $ is $ 40\% $

**Note**: One must know the concepts of mean or average and percentages in order to attempt the given question and provide a reasonable answer to the problem. One must check upon the calculations and tedious steps in order to recheck the answer.

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