Average
In Maths, an average of a list of data is the expression of the central value of a set of data. Mathematically, it is defined as the ratio of summation of all the data to the number of units present in the list. In terms of statistics, the average of a given set of numerical data is also called mean. For example, the average of 2, 3 and 4 is (2+3+4)/3 = 9/3 =3. So here 3 is the central value of 2,3 and 4. Thus, the meaning of average is to find the mean value of a group of numbers.
| Average = Sum of Values/Number of Values |
In this article, we are going to learn the definition of average, symbol, average formula in Maths, and steps to calculate the average, and many solved examples in detail.
Average Definition
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 set.
Check: Mean Definition
The average formula has many applications in real life. Suppose if we have to find the average age of men or women in a group or average male height in India, then we calculate it by adding all the values and dividing it by the number of values.
Symbol
The average is basically the mean of the values which are represented by x̄. It is also denoted by the symbol ‘μ’.
Average Formula in Maths
The formula to find the average of given numbers or values is very easy. We just have to add all the numbers and then divide the result by the number of values given. Hence, the average formula in Maths is given as follows:
Average = Sum of Values/ Number of values
Suppose, we have given with n number of values such as x1, x2, x3 ,….., xn. The average or the mean of the given data will be equal to:
Average = (x1+x2+x3+…+xn)/n
How to Calculate Average?
We can easily calculate the average for a given set of values. We just have to add all the values and divide the outcome by the number of given values.
Average can be calculated using three simple steps. They are:
Step 1: Sum of Numbers:
The first step in finding the average of numbers is to find the sum of all the given numbers.
Step 2: Number of Observations:
Next, we have to count how many numbers are in the given dataset.
Step 3: Average Calculation:
The final step in calculating the average is to divide the sum by the number of observations.
Now, let us consider an example to calculate the average.
If there are a group of numbers say, 20, 21, 23, 22, 21, 20, 23. Then find the average of these values.
By average formula, we know,
Average = (Sum of values)/No.of values
= (20+21+23+22+21+20+23)/7
= 150/7
=21.42
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