Definition of Average Formula
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.
- where ai = ith 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 a1, a2, ….., an corresponding to 1st observation, 2nd observation,…., nth 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 = (a1 + a2 + …. + an) / n
Examples
Example #1
Let us take an example of John who enrolled for the graduation program for environmental science. The three-year degree course is divided into six semesters and the final average percentage is calculated on the basis of the percentages scored in all the semesters. Calculate John’s final percentage on the basis of his following score:
Below is given data for calculation of the average percentage.
Given,
a1 = 79%, a2 = 81%, a3 = 74%, a4 = 70%, a5 = 82%, a6 = 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 of Average Formula
As the name “average” suggests, it refers to the central point among a set of observations and when it is utilized in the field of mathematics it represents the number which is typically mean of a group of numbers. The term is used often to express a number which is the representation for 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 central tendency theory.
Recommended Articles
This has been a guide to Average Formula. Here we discuss how to calculate the average using its formula along with examples and downloadable excel template. You can learn more about financing from the following articles –
- What is the Formula of Moving Average?
- What is EWMA?
- What is Central Tendency?
- Average vs Weighted Average – Compare and contrast
- Calculate Moving Average in Excel
- Calculate Mode in Excel
- AVERAGE Function in Excel
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