# Calculation of Mean in Discrete Series | Formula of Mean

Last Updated : 17 Aug, 2023

## 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 seriesÂ (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 Î£f.

#### 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:

## 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.

Â

#### Solution:

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

Â

MeanÂ = 9.42

#### Example 2:

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

Â

Â

MeanÂ = 56

#### Example 3:

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

Â

#### Solution:

Suppose the missing frequency is f.

Â

952 + 28f = 1,030 + 15f

28f – 15f = 1,030 – 952

13f = 78

f = 6

Missing Frequency = 6

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