Find the average of any given sequence of numbers using our interactive, online calculator. Use the tool below to input your numbers and press calculate to find the average.
What is an average?
The average, mathematically known as the arithmetic mean of a group of observations is the value that is equally shared out among all the observations. In simple terms, it is the average of a set of numbers. So, we can define average as –
The average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the given set.
Examples of Average
We use average in referring to many values in our everyday lives.
For example,
We usually say that the average number of runs scored by a player in this match was 20.
My average score in the exam was 65.
How is the average calculated?
It is quite simple to calculate the average of a given set of numbers. The average is calculated by adding all the data values and dividing them by the number of the data point. In other words, in order to find the average of a given set, we just need to add all the numbers and divide the result by the total count of numbers. How, do we represent this in the form of a formula?
The formula for finding average
Thus, if x1, x2, x3, ….…. xn are the values of n observations then the average of these observations is given by
Average = $\frac{x_1+ x_2+ x_3 + ……+ x_n}{n}$
Now, that we know that formula, we can write down the steps involved for finding the average of a given set of numbers.
Steps for finding the average of numbers
Below are the steps that should be carried out in order to find the average of a fixed set of numbers
Step 1 – Number of observations
The first step is to find the total number of observations given in the set. Let this total number be represented by “ n “.
Step 2 – Finding the sum of numbers
The second step for finding the average is to find the sum of all the numbers given to us. This means that if we have n numbers, say x1, x2, x3, ….…. and xn , then in the second step we need to find x1 + x2 + x3 + ….…. + xn.
Step 3 – Calculating the average
The third and final step is to calculate the average using the values that have been calculated in the previous two steps. Recall that the formula for finding the average of numbers is given by –
Average = $\frac{x_1+ x_2+ x_3 + ……+ x_n}{n}$
Also, in the previous two steps, we have already calculated the numerator as well as the denominator as required in this formula. Therefore, the only thing that we need to do is now is divide the sum obtained in the second step by the count of observations that we found in the first step.
Let us understand it through an example.
Example
If the heights of 5 persons are 144 cm, 152 cm, 151 cm, 158 cm and 155 cm respectively. Find the average height.
Solution
We have been given that the heights of 5 persons are 144 cm, 152 cm, 151 cm, 158 cm and 155 cm respectively.
The observations, in this case, are – 144 cm, 152 cm, 151 cm, 158 cm and 155 cm
Total number of observations = 5
To calculate the mean first we need to find the sum of all the observations.
Therefore,
(144 + 152 + 151 + 158 + 155) cm = 760 cm
Now, according to the formula of the average of numbers,
Average = $\frac{Sum\: of\: all\: observations}{Number\: of\: observations}$
Therefore,
Average = cm = 152 cm
Hence, the average height of the 5 persons = 152 cm
How to use the average calculator?
Using the average calculator is quite simple. You just need to enter all the values given, separated by commas and click on the calculate button. The rest will be done by the calculator and you will get the average.
Finding the average of whole numbers
Let us understand it by an example.
Suppose we have a group of 7 numbers, say, 20, 21, 23, 22, 21, 20, 23 and we want to find the average of these numbers.
If we wish to find the average of these numbers using the formula, we will have,
Total count of numbers = 7
Sum of the numbers = 20 + 21 + 23 + 22 + 21 + 20 + 23 = 150
Now, using the formula for average of number we have,
Average = $\frac{Sum\: of\: all\: observations}{Number\: of\: observations}$ = $\frac{150}{7}$ = 21.429
Hence, the average of the given set of numbers is 21.429.
Now, let us find the average of these numbers using the calculator. In order to do so, we just need to enter the given value, separated by commas, space or a new line under the heading that says “ Input for Average calculation “. Below is the snapshot of how we would enter these numbers in the average calculator –
Next, we will click on the calculate button and we can check the result under the heading “ Average “ below is a snapshot of the result that would appear in the calculator –
Now, that we have seen how to find the average of a given set of whole numbers, let us discuss about finding the average of decimal numbers.
Finding the average of decimal numbers
While finding the average of whole numbers is fast and easy, doing the same for decimal numbers can be trickier as well as needs time. Let us see how the average calculator helps us check our results when we wish to find the average of decimal numbers.
Let us understand it by an example.
Example
If the heights of males in a group are 5.5, 5.3, 5.7, 5.9, 6, 5.10, 5.8, 5.6, 5.4, 6 then find the average height.
If we wish to find the average of these numbers using the formula, we will have,
Total count of numbers = 10
Sum of the numbers = 5.5 + 5.3 + 5.7 + 5.9 + 6 + 5.10 + 5.8 + 5.6 + 5.4 + 6 = 56.3
Now, using the formula for the average of numbers we have,
Average = $\frac{Sum\: of\: all\: observations}{Number\: of\: observations}$ = $\frac{56.3}{10}$= 5.63
Hence, the average of the given set of numbers is 56.3.
Now, let us find the average of these numbers using the calculator. In order to do so, we just need to enter the given value, separated by commas, space or a new line under the heading that says “ Input for Average calculation “. Below is the snapshot of how we would enter these numbers in the average calculator –
Next, we will click on the calculate button and we can check the result under the heading “ Average “ below is a snapshot of the result that would appear in the calculator –
What are the advantages of using an average calculator?
The following are the advantages of using an average calculator –
- Fast and easy to calculate
- Sensitive to extreme values