[Maths Class Notes] on Arithmetic Mean Formula Pdf for Exam

According to statistics, the arithmetic mean is the ratio of all observations in a data set to the total number of observations. For instance, the average rainfall of a place and the average salary of an organization’s employees can be used. A lot of time, we hear statements like “the average family income is ₹15,000 or there is about 1000 mm of rain every month in a certain area.”. Average is also referred to as Arithmetic Mean.

What Does Arithmetic Mean?

In mathematics, the arithmetic mean is usually referred to as the mean or as an average. An arithmetic mean is calculated by adding all the numbers in a set of data and then dividing by the number of items included in the set. As a result, the middle number is the arithmetic mean for equally distributed numbers. As an added bonus, there are numerous ways to calculate the arithmetic mean, which is based on the amount of data and the distribution of that data.

Let’s take a look at an example where the arithmetic mean is used. Since 6 + 8 + 10 = 24, and 24 divided by 3 (there are three numbers) is 8, the mean of the numbers 6, 8, 10 is 8. During a particular month, the arithmetic mean continues to be used to calculate the average closing price of a stock. In the example, suppose there are 24 trading days in a month. Where would we find the mean? The arithmetic mean can be calculated by adding all the prices together and dividing by 24.

Calculation of Arithmetic Mean

The arithmetic mean is derived using the mathematical formula below.

Where,

 

A- arithmetic mean or average

n- number of items or terms being averaged

x1– value of every single item in the list of numbers being averaged

 

A= [frac {1} {n}] × ⁿ ∑_i=0 xi

 

Here is a more understandable version of the arithmetic mean formula.

A= [frac {S} {N}]

Where,

A- Arithmetic mean or average.

n- number of items or terms being averaged.

S- The sum total of the numbers in the set of interest being averaged.

Arithmetic Mean for Ungrouped Data

Using the formula below, we calculate the arithmetic mean:

Mean x̄ = Sum of all observations / Number of observations

Example: Calculate the arithmetic mean of the first six odd, natural numbers.

The first six odd, natural numbers are: 1, 3, 5, 7, 9, 11.

The formula [frac {(1+3+5+7+9+11)} {6}] =

[frac {36} {6}]  = 6.

As a result, the arithmetic mean is 6.

Arithmetic Mean for Grouped Data

To determine the arithmetic mean of grouped data, three methods are available (Direct method, Short-cut method, and Step-deviation method). According to the numerical values of xi and fi, the method to be used must be chosen. The sum of all data inputs is xi, and the sum of their frequencies is fi. ∑ represents the summation. Direct methods work when xi and fi are sufficiently small. When the values are large, we use the assumed arithmetic mean method or the step deviation method.