What is Arithmetic Mean?
Arithmetic Mean, commonly used term in statistics, is the average of the numerical values set and is calculated by firstly calculating the sum of number in the set and then dividing resultant by count of those numbers.
Arithmetic Mean Formula
The formula is represented as below :
Where,
 x_{1, }x_{2, }x_{3, }x_{n }are the observations
 n is the number of observations
Alternatively, it can be symbolically written as shown below
In the above Equation, the symbol ∑ is known as sigma. It implies the summation of the values.
Steps to Calculate Arithmetic Mean
 Step 1: Calculate the sum of all the observations.

 x_{1 }+ x_{2 }+ x_{3 }+…….+ 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 five 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, the calculation is as follows,
 =56+44+20+50+80/5
Example #2
Franklin Inc. is a manufacturing concern with ten 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 calculate the arithmetic mean of salary of workers in the company. The following table gives the wages along with the names of the workers.
Name of the Worker  Wages ($) 
Jeffery Gates  100 
George Clinton  120 
Thomas Smith  250 
Kamala Sanders  90 
Steve Roosevelt  110 
Martha Smith  40 
Clara Truman  50 
Nicholas Obama  150 
Michael Carlin  70 
Arnold Smith  100 
Number of Observations (n)  10 
Calculate the arithmetic mean of wages for the CEO.
Solution
Therefore, the calculation is as follows,
 =(100+120+250+90+110+40+50+150+70+100+10)/10
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 have had a better teacher. These are the marks of 7 students each studying in the two Divisions.
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Sr. No  Division A  Division B 
Student 1  56  70 
Student 2  60  65 
Student 3  56  60 
Student 4  64  65 
Student 5  70  75 
Student 6  55  55 
Student 7  50  65 
Find out which Division has higher arithmetic mean.
Solution
Division A
Therefore, the calculation is as follows,
 =(56+60+56+64+70+55+50)/7
 =58.71 marks
Division B
Therefore, the calculation is as follows,
 =(70+65+60+65+75+55+65)/7
 = 65 marks
The arithmetic mean of Division A is 58.71 marks, and for Division B is 65 marks (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.
Analyst  Target Price 
A  1000 
B  1200 
C  900 
D  900 
E  1500 
F  750 
G  750 
Solution
In Excel, there is an inbuilt formula to calculate the 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 statistics and is most commonly used as the most popular measure of central tendency. It is straightforward to calculate and does not require knowledge of highend statistics. It is used when all observations in the data set are equally important. If some statements 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 a downloadable excel template. You can learn more about excel modeling from the following articles –
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