Average Formula

Average Formula – Table of Contents

• What is the Average Formula?
• Examples

What is the Average Formula?

The term “average” refers to the mathematical mean calculated for a set of observations. The formula for average is calculated by adding all the observations and then divide the result by the number of observations.

Mathematically, Average Formula is represented as,

where a_i = i^th observation

n = Number of observations

Further, the weighted average formula is calculated by initially multiplying each observation by its corresponding weighting, then adding up all the weighted observation and then divide the result by the sum of the weightings.

Mathematically, it is represented as,

where w_i = weight of the i^th observation

a_i = i^th observation

It can be said that the simple average is a case where all weights of each observation are equal to one, i.e. w₁ = w₂ = …. = w_n = 1.

Explanation of the Average and Weighted Average Formula

The formula for 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, ….., 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 formula for average is calculated by adding all the observations and then divide the result by the number of observations as shown below.

Average = (a₁ + a₂ + …. + a_n) / n

The formula for weighted average formula can be calculated by using the following steps:

Step 1: Firstly, determine the observation and they are denoted by a₁, a₂, ….., a_n corresponding to 1^st observation, 2^nd observation,…., n^th observation.

Step 2: Next, determine the weightings corresponding to each observation and they are denoted by w₁, w₂, ….., w_n.

Step 3: Next, multiply each observation by its corresponding weighting and then add up all the weighted observations.

Step 4: Finally, the formula for weighted average is calculated by dividing the sum of all the weighted observations by the sum of all the weights as shown below.

Weighted Average Formula = (w₁ * a₁ + w₂ * a₂ + …… + w_n * a_n) / (w₁ + w₂ +….. + w_n)

Examples of Average Formula (with Excel Template)

Let’s see some simple to advanced examples of Average formula to understand it better.

Example #1

Let us take an example of John who enrolled for 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.

Example #2

Let us assume that the university changed its scoring policy recently wherein it has shifted from a simple average scoring to weighted average scoring. As per the new policy, 1^st and 2^nd semester will be weighed at 5% each, 3^rd and 4^th semester at 15% each, and 5^th and 6^th semester at 30% each. Based on the new scoring system, calculate the final average for John during his graduate program.

Below is given data for calculation of the weighted average in excel.

Given,

• w₁ = 5%, w₂ = 5%, w₃ = 15%, w₄ = 15%, w₅ = 30%, w₆ = 30%,
• 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,

•  Weighted Average Formula = (5% * 79% + 5% * 81% + 15% * 74% + 15% * 70% + 30% * 82% + 30% * 85%) / (5% + 5% + 15% + 15% + 30% + 30%)

Average will be –

•  Average = 79.70%

Therefore, John’s average graduation percentage comes to be 79.7% as per the new scoring policy.

Relevance and 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. The formula for average 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 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