Arithmetic Mean

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 :

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For eg:
Source: Arithmetic Mean (wallstreetmojo.com)

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.

• x₁ + x₂ + x₃ +…….+ x_n

• 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.

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 exchangesThe Stock ExchangesStock exchange refers to a market that facilitates the buying and selling of listed securities such as public company stocks, exchange-traded funds, debt instruments, options, etc., as per the standard regulations and guidelines—for instance, NYSE and NASDAQ.read more. Different analysts have given their target price of the stockTarget Price Of The StockPrice Target in the context of stock markets, means the expected valuation of a stock in the coming future and the valuation may be done either by the stock analysts or by the investors themselves. For an investor, price target reflects the price at which he will be willing to buy or sell the stock at a particular period of time or mark an exit from their current position.read more. 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 in-built 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 tendencyCentral TendencyCentral Tendency is a statistical measure that displays the centre point of the entire Data Distribution & you can find it using 3 different measures, i.e., Mean, Median, & Mode.read more. It is straightforward to calculate and does not require knowledge of high-end statisticsStatisticsStatistics is the science behind identifying, collecting, organizing and summarizing, analyzing, interpreting, and finally, presenting such data, either qualitative or quantitative, which helps make better and effective decisions with relevance.read more. 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 –

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