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Mean, Median and Mode| Comparison, Relationship and Calculation
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Calculation of Mode by Graphical Method

Last Updated : 05 Jun, 2024
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The word mode is derived from the French word 'La Mode', meaning anything that is in fashion or vogue. A measure of central tendency in statistical series that determines the value occurring most frequently in the given series is known as mode. In other words, the modal value of the series has the highest frequency in the given series.

For example, if in a class of 100 students, 20 students have opted for Mathematics, 50 students have opted for IP, and the rest 30 have opted for Physical Education, then the modal opted subject of the class would be IP. 

Mode by Graphical Method

The mode for a given set of series can be located through a histogram. The steps to locate mode through Graph are as follows:

Step 1

Draw a histogram of the given set of series. 

Step 2

The rectangle of the histogram with the greatest height will be the modal class of the series. 

Step 3

Draw a line joining the top left corner/point of the rectangle of the modal class to the top left corner/point of the rectangle of the succeeding class.

Step 4

Similarly, draw a line joining the top right corner/point of the rectangle of the modal class to the top right corner/point of the rectangle of the preceding class. 

Step 5

Draw a line perpendicular to the X-axis from the intersection point of the two lines drawn in the previous two steps. 

Step 6

The point at which the perpendicular line cuts the X-axis is the modal value of the given series. 

Example 1: 

Determine mode of the following series, using the Graphic Method.

Solution:

Verification: The modal value can be verified with Inspection Method.

The formula for calculating Mode through Inspection Method is,

Z=l_1+\frac{f_1-f_0}{2f_1-f_0-f_2}\times{i}

f_1=17,~f_0=9,~f_2=9,~and~i=8

Z=30+\frac{20-10}{2(20)-10-15}\times{10}

=30+\frac{10}{40-25}\times{10}

= 30 + 6.67

= 36.67

Example 2:

Determine mode of the following series, using the Graphic Method.

Class Interval

0-5

5-10

10-15

15-20

20-25

25-30

30-35

Frequency

8

4

10

25

15

30

12

Solution:

Verification: The modal value can be verified with Inspection Method.

The formula for calculating Mode through Inspection Method is,

Z=l_1+\frac{f_1-f_0}{2f_1-f_0-f_2}\times{i}

f_1=17,~f_0=9,~f_2=9,~and~i=8

Z=25+\frac{30-15}{2(30)-15-12}\times{5}

=25+\frac{15}{60-27}\times{5}

= 25 + 2.27

= 27.27

Also Read:

  • Mode: Meaning, Formula, Merits, Demerits, and Examples
  • Calculation of Mode in Individual Series | Formula of Mode
  • Calculation of Mode in Discrete Series | Formula of Mode
  • Grouping Method of Calculating Mode in Discrete Series | Formula of Mode
  • Calculation of Mode in Continuous Series | Formula of Mode
  • Calculation of Mode in Special Cases

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Mean, Median and Mode| Comparison, Relationship and Calculation

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Article Tags :
  • Statistics for Economics
  • Commerce
  • Commerce - 11th

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    What is Coefficient of Variation? As Standard Deviation is an absolute measure of dispersion, one cannot use it for comparing the variability of two or more series when they are expressed in different units. Therefore, in order to compare the variability of two or more series with different units it
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    Lorenz Curveb : Meaning, Construction, and Application
    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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    The previous statistical approaches (such as central tendency and dispersion) are limited to analysing a single variable or statistical analysis. This type of statistical analysis in which one variable is involved is known as Univariate Distribution. However, there are instances in real-world situat
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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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