Arithmetic Mean Formula

Formula to Find Arithmetic Mean

The arithmetic mean is a measure of central tendency which is calculated by dividing the sum of the observations divided by the number of observations. The arithmetic mean is also known as mean or average. The Arithmetic Mean formula is represented as below :

Where,

• x_1, x_2, x_3, x_n are the observations
• n is the number of observations

Alternatively, the Arithmetic Mean Formula can be symbolically written as shown below-

In the above Arithmetic Mean Equation, the symbol  ∑ is known as sigma. It implies the summation of the values.

Steps to Calculate Arithmetic Mean

In order to calculate the arithmetic mean, use the following steps:

• Step 1: Calculate the sum of all the observations.

• • x₁ + x₂ + x₃ +…….+ x_n
• Step 2: Determine the number of observations. The number of observations is denoted by n.
• Step 3: Calculate the arithmetic mean using:

• • Arithmetic Mean = x1+x2+x3+…………….+xn/n
  • Alternatively, Arithmetic Mean Formula in symbolic terms is represented as below,

Examples

Example #1

There are 5 observations. These are 56, 44, 20, 50, 80. Find their arithmetic mean.

Solution

• Here, the observations are 56, 44, 20, 50, 80.
• n = 5

Therefore,  calculation of arithmetic mean is as follows,

• =56+44+20+50+80/5

Arithmetic Mean will be – 

• =50
• The arithmetic mean is 50.

Example #2

Franklin Inc. is a manufacturing concern with 10 workers. There are negotiations between the management of Franklin Inc. and its trade union regarding wages. For this purpose, the CEO of Franklin Inc. wants to do the calculation of the arithmetic mean of wages of workers in the company. The following table gives the wages along with the names of the workers.

Calculate the arithmetic mean of wages for the CEO.

Solution

Therefore, the calculation of arithmetic mean is as follows,

• =(100+120+250+90+110+40+50+150+70+100+10)/10

Arithmetic Mean will be – 

• =108

The arithmetic mean of wages is $108.

Example #3

The Principal of a school calls two teachers to his office – one teaches Division A and the other teaches Division B. Both of them claim that their teaching methods are superior. The Principal decides that the Division which has a higher arithmetic mean of marks will be considered to have had a better teacher. These are the marks of 7 students each studying in the two Divisions.

Find out which Division has higher arithmetic mean.

Solution

Division A

Therefore, the calculation of arithmetic mean is as follows,

• =(56+60+56+64+70+55+50)/7

Arithmetic Mean will be – 

• =58.71 marks

Division B

Therefore, the calculation of arithmetic mean is as follows,

• =(70+65+60+65+75+55+65)/7

Arithmetic Mean will be – 

• = 65 marks

The arithmetic mean of Division A is 58.71 marks, while the arithmetic mean of Division B is 65 marks. The arithmetic mean of Division B is higher.

Arithmetic Mean in Excel

There is company Grandsoft Inc. which is listed on the stock exchanges. Different analysts have given their target price of the stock. Calculate the arithmetic mean of the stock prices.

Solution

In Excel, there is an in-built formula to calculate the arithmetic mean.

Step #1 – Select a blank cell and type =AVERAGE(B2: B8)

Step #2 – Press Enter to Get the Answer

Relevance and Uses

The arithmetic mean is one of the most important measures in statistics. The arithmetic mean is the most commonly used as the most popular measure of central tendency. Arithmetic Mean is very simple to calculate. It does not require knowledge of high-end statistics. It is much easier to calculate as compared to say geometric mean or harmonic mean. In the majority of the cases, it does not require the use of a computer as it is easy to calculate. Arithmetic Mean takes all the observations into consideration which implies that no observation is left out. This is where arithmetic means scores over median and mode. The results obtained from large groupings of numbers are also reliable when we use the arithmetic mean. Mean can be subject to further algebraic treatment.

When different samples are taken from the same population, arithmetic mean is known to have less fluctuation. The arithmetic mean is used when all observations in the data set are equally important. If some observations are more important than others, then a weighted mean is used.

Recommended Articles

This has been a guide to Arithmetic Mean Formula. Here we discuss the calculation of arithmetic mean using its formula along with practical examples and downloadable excel template. You can learn more about excel modeling from the following articles –

• Exponents in Excel
• Formula of Compounding
• Formula of Moving Average
• Weighted Average Excel