**Formula of Arithmetic Mean (Table of Contents)**

## What is the Arithmetic Mean Formula?

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 :

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

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.

### Explanation of Arithmetic Mean Formula

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

**Step 1: **Calculate the sum of all the observations. This is calculated by the formula:

x_{1 }+ x_{2 }+ x_{3 }+…….+ x_{n}

**Step 2:** Determine the number of observations. The number of observations is denoted by n.

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**Step 3: **Calculate the arithmetic mean using the formula:

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

Alternatively, Arithmetic Mean Formula in symbolic terms is represented as below,

### Examples of Arithmetic Mean Formula

Let’s understand some simple to advanced examples of the Arithmetic Mean Equation in a better manner.

#### Arithmetic Mean – 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.

#### Arithmetic Mean – 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.

#### Arithmetic Mean – 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 Formula 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 the formula =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 Formula 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 Formula 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.

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

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