# Arithmetic Mean Formula

Arithmetic Mean Formula – The arithmetic mean formula computes the mean or average of the numbers and is used to determine the central tendency of the data. It may alternatively be defined as the sum of all provided observations over the entire number of observations. Let us examine the arithmetic mean formula with solved examples.

## Arithmetic Mean Formula

Arithmetic Mean OR (AM) is determined by adding all of the supplied values and then dividing by the number of values. For equally distributed words organised in ascending or descending order, the arithmetic mean is the sequence’s middle term. The arithmetic mean is also known as mean, average, or arithmetic average.

The Arithmetic Mean Formula is used for finding the mean of data provided to students. This Arithmetic Mean Formula is most commonly used in Statistics and Economics. The formula uses the number of observations divided by the total number of observations to find the arithmetic mean of the equation.

The Arithmetic Mean is the sum of all the integers in a group divided by the number of items in that list. For example, the mean of the numbers 7, 9, and 11 is 4, since 7 + 9 + 11 = 27, and 27 divided by 3 is 9.

$$\LARGE \overline{X}=\frac{\sum_{i=1}^{n}X_{i}}{N}$$
Where N is the total number of observations.

## What is Arithmetic Mean Formula?

The Arithmetic Mean Formula has been provided for use by students in various classes and practical purposes.

### 1] Individual Series

The Arithmetic Mean Formula can be used to determine the mean of the series for this type of series. The formula can be applied to this type of progression called Individual series.

### 2] Discrete Series

This is another type of arithmetic progression. The Arithmetic Mean Formula can be applied to this type of progression called discrete series.

### 3] Continuous Series

This type of progression is another type of series. The Arithmetic Mean Formula can be applied to this type of progression called continuous series.

## Steps to calculate Arithmetic Mean

By knowing how the Arithmetic Mean Formula was created, students will have a better grasp of why it is so important that they study it. Studying the formula for Arithmetic Mean derivation can help students have a better understanding of its historical roots and potential uses. Students will be able to rapidly apply the technique to find solutions to different kinds of mathematical and statistical problems. Students who understand the roots of the formula will be able to modify it or use it in different situations to calculate the mean of any kind of series. We can calculate the arithmetic mean by using the steps discussed below,

Step 1: Find the sum of all the values of the data set.

Step 2: Count the number of the values of the data set (say n)

Step 3: Divide the sum obtained in step 1 with the n from step 2 to get the arithmetic mean.

## Limitations of the Arithmetic Mean

Every formula has limitations to how it can be used to make things easier for students. As students know, nothing is perfect and everything exists with errors. The Arithmetic Mean Formula also has quite a lot of limitations just like other formulas.

## Arithmetic Mean Solved Examples

Example 1: Calculate the arithmetic mean of the first five even numbers.

Solution: Arithmetic mean of first five even numbers,

First Five Even Numbers = 2, 4, 6, 8 and 10

Number of observations (n) = 5

Mean (x̄) = (Sum of Observations)/ (Number of Observations)

x̄  = (2 + 4 + 6 + 8 + 10)/5 = 30/5

x̄ = 6

Hence, the arithmetic mean of the first five prime numbers is 6.

Example 2: If the arithmetic mean of five observations 30, 40, 50, x, and 70 is 50. Calculate the value of x.

Solution: Given, observations are 30, 40, 50, x, and 70

Number of observations = 5

Mean (x̄) = (Sum of Observations)/ (Number of Observations)

50 = (30 + 40 + 50 + x + 70)/5

250 = 190 + x

250 – 190 = x

x = 60

Hence, the value of x is 60

For students to learn how to correctly use the Arithmetic Mean Formula and how to creatively use it to find the best and simplest way to solve a problem, Extramarks has offered a number of instances of the formula that have been solved.

### 1. Why do students occasionally struggle to respond to a question?

Getting the wrong answer or finding a question challenging is not a big issue. Formulas may be challenging to comprehend and apply accurately on one’s first attempt. Students can turn to the NCERT solutions offered by Extramarks for assistance in these situations. Students can get a quick idea of the type of solutions provided by looking at NCERT solutions. Therefore, when learning, students must take the aid and assistance of NCERT solutions.

### 2. What is the formula of Arithmetic Mean?

The arithmetic mean formula is,

x̄ = (Sum of Observations)/ (Number of Observations)

where represents the arithmetic mean.

### 3. What is the Arithmetic Mean Formula for Grouped Data?

The arithmetic mean formula for the ungrouped data is,

x̄ = (x₁f₁+x₂f₂+……+xₙfₙ) / ∑fi

where,
is the arithmetic mean
f₁+ f₂ + ….fₙ = ∑fi indicates the sum of all frequencies