What does Arithmetic Mean?

Arithmetic Mean Formula

The formula is as below:

Arithmetic Mean = x1 + x2 + x3 +……+ xn / n

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Where,

  • x1, x2, x3, xn are the observationsn is the number of observations

Alternatively, one can symbolically write it as shown below:

In the above equation, the symbol ∑ 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 +…….+ xn

  • Arithmetic Mean = x1+x2+x3+…………….+xn/nAlternatively, the arithmetic mean formula in symbolic terms is 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 company’s arithmetic mean of workers’ salaries. The following table gives the wages along with the names of the workers.

Calculate the arithmetic mean of wages for the CEO.

Therefore, the calculation is as follows:

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

Example #3

The school principal 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 a better teacher. These are the marks of 7 students each studying in the two divisions.

Find out which division has higher arithmetic mean.

Division A

The calculation is as follows:

  • =(56+60+56+64+70+55+50)/7

  • =58.71 marks

Division B

  • =(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.

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. One may use it when all observations in the data set are equally important. A weighted mean is used if some statements are more important than others.

This article is a guide to Arithmetic Mean Formula. Here, we discuss the arithmetic mean calculation using its formula, practical examples, and a downloadable Excel template. You can learn more about Excel modeling from the following articles: –

  • Exponents in ExcelFormula of CompoundingFormula of Moving AverageFormula Of Moving AverageMoving Average (MA), commonly used in capital markets, can be defined as a succession of mean that is derived from a successive period of numbers or values and the same would be calculated continually as the new data is available. This can be lagging or trend-following indicator as this would be based on previous numbers.read moreWeighted Average ExcelWeighted Average ExcelIn Excel, we calculate Weighted Average by assigning weights to each data set. It is generally used to compute robust observations in statistics or portfolios and is calculated as (w1x1+w2x2+….+wnxn)/(w1+w2+..wn), where w is the weight allocated to the x value and the sumproduct function is used.read more