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Calculation of Mean in Continuous Series | Formula of Mean
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Calculation of Mean in Discrete Series | Formula of Mean

Last Updated : 08 Aug, 2024
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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

Related Articles

  • Calculation of Mean in Discrete Series | Formula of Mean
  • Calculation of Mean in Continuous Series | Formula of Mean

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.


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Calculation of Mean in Continuous Series | Formula of Mean

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    What is Lorenz Curve?The variability of a statistical series can be measured through different measures, Lorenz Curve is one of them. It is a Cumulative Percentage Curve and was first used by Max Lorenz. Generally, Lorenz Curves are used to measure the variability of the distribution of income and w
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    Chapter 9: Correlation

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    Methods of Measurements of Correlation
    What is Correlation?A statistical tool that helps in the study of the relationship between two variables is known as Correlation. It also helps in understanding the economic behaviour of the variables. However, correlation does not tell anything about the cause-and-effect relationship between the tw
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    Scatter Diagram Correlation | Meaning, Interpretation, Example
    What is a Scatter Diagram?A simple and attractive method of measuring correlation by diagrammatically representing bivariate distribution for determination of the nature of the correlation between the variables is known as the Scatter Diagram Method. This method gives the investigator/analyst a visu
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    Spearman's Rank Correlation Coefficient in Statistics
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    Karl Pearson's Coefficient of Correlation | Assumptions, Merits and Demerits
    What is Karl Pearson's Coefficient of Correlation?The first person to give a mathematical formula for the measurement of the degree of relationship between two variables in 1890 was Karl Pearson. Karl Pearson's Coefficient of Correlation is also known as Product Moment Correlation or Simple Correlat
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    Karl Pearson's Coefficient of Correlation | Methods and Examples
    What is Karl Pearson's Coefficient of Correlation?The first person to give a mathematical formula for the measurement of the degree of relationship between two variables in 1890 was Karl Pearson. Karl Pearson's Coefficient of Correlation is also known as Product Moment Correlation or Simple Correlat
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