Calculation of Mode by Graphical Method

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. 

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,

= 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,

= 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

What is the mode?

The mode is the value that appears most frequently in a dataset. For grouped data, the mode is the midpoint of the modal class, which is the class interval with the highest frequency.

What is the graphical method for finding the mode?

The graphical method for finding the mode involves creating a histogram of the frequency distribution and then using the highest bar (modal class) to estimate the mode by constructing a mode polygon or by using other interpolation techniques.

How do you interpret the intersection point for the mode?

The intersection point of the lines drawn from the tops of the bars adjacent to the modal class represents the mode. The x-coordinate of this intersection gives the approximate value of the mode.

What are the advantages of the graphical method?

Visual Representation: It provides a clear visual representation of the frequency distribution.

Easy to Understand: It is easy to understand and interpret, especially for non-technical audiences.

Quick Estimation: It allows for a quick estimation of the mode.

What are the limitations of the graphical method?

Approximation: The mode obtained is an approximation and may not be as precise as other statistical methods.

Manual Errors: Drawing errors and inaccuracies in the histogram can affect the mode calculation.

Not Suitable for All Data: It may not be practical for large datasets or datasets with many class intervals.

Can the graphical method be used for ungrouped data?

The graphical method is primarily used for grouped data. For ungrouped data, it’s usually easier and more accurate to identify the mode by simply counting the frequency of each value.