## Formula to Calculate Average

Average is the value that is used to represent the set of values of data as is the average calculated from whole data and this formula is calculated by adding all the values of the set given, denoted by summation of X and dividing it by the number of values given in set denoted by N.

**Average = (a**

_{1}+ a_{2}+ …. + a_{n}) / n- where a
_{i}= i^{th}observation - n = Number of observations

### Explanation

**The calculation of average can be calculated by using the following steps:**

**Step 1:**Firstly, determine the observation, and they are denoted by a_{1}, a_{2}, ….., a_{n}corresponding to 1^{st}observation, 2^{nd}observation,…., n^{th}observation.**Step 2:**Next, determine the number of observations, and it is denoted by n.**Step 3:**Finally, the average is calculated by adding all the observations and then divide the result by the number of observations, as shown below.

**Average = (a _{1} + a_{2} + …. + a_{n}) / n**

### Examples

#### Example #1

**Let us take an example of John, who enrolled in the graduation program for environmental science. The three-year degree course is divided into six semesters, and the final average percentage is calculated based on the percentages scored in all the semesters. Calculate John’s final percentage based on his following score:**

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Below is given data for calculation of the average percentage.

**Given,**

a_{1} = 79%, a_{2} = 81%, a_{3} = 74%, a_{4} = 70%, a_{5} = 82%, a_{6} = 85%, n = 6

Using the above information, the calculation of average will be as follows,

- Average = (79% + 81% + 74% + 70% +82% + 85%) / 6

**Average will be –**

- Average =
**78.50%**

Therefore, David scored a final percentage of 78.5% in the graduation program.

### Uses

As the name “average” suggests, it refers to the central point among a set of observations. When it is utilized in mathematics, it represents the number which is typically mean of a group of numbers. The term is often used to express a number, which represents a group of people or things. It is very important because it helps in summarising a large number of data into a single value, and it also indicates that there is some inconsistency around the single value within the original data, which forms a very crucial part of the central tendency theory.

### Recommended Articles

This has been a guide to Average Formula. Here we discuss how to calculate the average using its formula and examples and a downloadable excel template. You can learn more about financing from the following articles –

- Moving Average Formula
- Measures of Central Tendency
- Average vs Weighted Average
- AVERAGE Function in Excel
- Effect Size

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