Calculation of Mean in Discrete Series | Formula of Mean (original) (raw)

Last Updated : 23 Jul, 2025

What is Mean?

Mean is the sum of a set of numbers divided by the total number of values. It is also referred to as the **average. **For instance, if there are four items in a series, i.e. 2, 5, 8, 3, and 9. The simple arithmetic mean is (2 + 5 + 8 + 3 + 9) / 5 = 5.4.

What is Discrete Series?

In discrete series ****(ungrouped frequency distribution)**, the values of variables represent the repetitions. It means that the frequencies are given corresponding to the different values of variables. The total number of observations in a discrete series, N, equals the sum of the frequencies, which is Σf.

Example of Discrete Series

If 6 students of a class score 50 marks, 4 students score 60 marks, 7 students score 70 marks, 3 students score 80 marks, and 5 students score 90 marks, then this information will be shown as:

Marks Number of Students
50 6
60 4
70 7
80 3
90 5

Mean in Discrete Series:

Mean in discrete series can be calculated by using:

  1. Direct Method;
  2. Short-Cut Method; and
  3. Step Deviation Method

Example 1:

Find the average of the following discrete series using any of the three methods.

Mean in Discrete Series

Solution:

We will be using Direct Method to determine Mean of the given series.

Mean in Discrete Series

\bar{X}=\frac{\sum{fX}}{\sum{f}}

\bar{X}=\frac{264}{28}

**Mean (\bar{X}) **= 9.42

Example 2:

Determine the arithmetic mean from the following frequency table using Step-Deviation Method:

Mean in Discrete Series

Solution:

Mean in Discrete Series

\bar{X}=A+\frac{\sum{fd'}}{\sum{f}}\times{C}

\bar{X}=60+\frac{(-20)}{50}\times{10}

**Mean (\bar{X}) = **56

Example 3:

If the mean of the following distribution is 28, locate the missing frequency.

Mean in Discrete Series

Solution:

Suppose the missing frequency is f.

Mean in Discrete Series

\bar{X}=\frac{\sum{fX}}{\sum{f}}

28=\frac{1,030+15f}{34+f}

952 + 28f = 1,030 + 15f

28f - 15f = 1,030 - 952

13f = 78

f = 6

**Missing Frequency = 6

Summary

The mean, or average, of a set of numbers is calculated by dividing the sum of the numbers by the total count of values. In discrete series, the frequencies of different values are considered, and various methods like Direct, Short-Cut, and Step-Deviation are used to find the mean.