Frequency Polygon Graph, Uses and Illustrations

Q: How many types of frequency polygons are there?

The following are different types of frequency polygons: Simple Frequency Polygon: This is a standard form that connects the midpoints of tops of the bars in a histogram with straight lines. Relative Frequency Polygon: This type of frequency polygon uses relative frequencies (proportions or percentages) instead of using absolute frequencies. This frequency polygon is used for comparing datasets of different sizes. Cumulative Frequency Polygon (Ogives): Ogives are related and they represent cumulative frequencies. These can be used for showing the cumulative distribution of data and are used with frequency polygons. Smoothed Frequency Polygon: Rather than connecting points with straight lines, smoothed curves or splines might are used to give a more continuous appearance to data distribution. Overlayed Frequency Polygons: Multiple frequency polygons can be overlaid on same graph for comparing different datasets or distributions.

Updated on Jul 25, 2025 15:01 IST

By Jaya Sharma, Assistant Manager - Content

A frequency polygon is a graph used for representing the frequencies of different classes in the dataset. It is used to display the shape of the distribution of continous variable. The data is organised into frequency distribution tabke which lists classes or intervals of data and their corresponding frequencies.

For every class, a point is plotted at midpoint of class interval on the x-axis and at frequency of class on the y-axis. This lesson provides a detailed coverage of frequency distribution from the statistics chapter. Students who want to learn more about this topic in detail from exam point of view must check out NCERT solutions of statistics chapter.

Table of content

What is a Frequency Polygon?
What are the Uses of Frequency Polygons?
How To Draw Frequency Polygon?
Illustrated Examples on Frequency Polygons
FAQs on frequency polygon

What is a Frequency Polygon?

Frequency represents quantitative data. By joining the centre points of a histogram's rectangles, the diagram or figure so formed is known as a frequency polygon. You can observe a slope, which denotes the rate of change (increase/decrease) in the value. Thus, a frequency polygon is a graph constructed by joining the midpoints of each interval. A frequency polygon is the sum of all frequencies.

From the above diagram, we can say the area ABCDEFGH is the frequency polygon for the data corresponding to the image's right side.

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What are the Uses of Frequency Polygons?

Frequency polygons have a number of applications that have been explained below:

Analysis of Data distribution: Frequency polygons give a clear visual representation of dataset distribution. These polygons help in identifying distribution shape that may be normal, skewed or bimodal. IIT JAM entrance exam often ask questions related to this application.
Comparative analysis: These are used for comparing multiple datasets' distribution on the same graph. This helps in visualising the differences and similarities between groups or across different conditions.
Trend analysis: By plotting frequency polygons for the data that has been collected over different periods of time, analysts can observe trends as well as the changes in the data distribution over time.
Finding outliers: Frequency polygons can identify potential outliers in the data since such observations appear as distinct deviations from the entire shape of the polygon.
Education: Students can easily understand the concept of data distribution, central tendency and variability through frequency polygons. JEE Main exam aspirants can prepare well for the exam by learning about these polygons.
Market research: These polygons are used for visualising the survey data, customer feedback score, as well as other metrics for understanding the distribution of responses.

How To Draw Frequency Polygon?

You need to follow the procedure that has been listed below. IISER exam and GATE exam aspirants must know how to draw a frequency polygon. However, before drawing frequency polygons, you need to construct a histogram:

Step 1: Select a class interval and indicate the values on axis.

Step 2: Label the horizontal axes with the midpoint of each interval.

Step 3: Now, you need to label the vertical axes with class frequency.

Step 4: Mark a point at height in the centre of every class interval as per the frequency of every class interval
Step 5: Use a line segment to join these spots.
Step 6: The representation obtained is the frequency polygon.

Illustrated Examples on Frequency Polygons

Let us consider some examples related to frequency polygons:

1. Consider the marks, out of 100, obtained by 51 students of a class in a test, given in the table. Draw a frequency polygon corresponding to this frequency distribution table.

Marks	Number of students
0-10	5
10-20	10
20-30	4
30-40	6
40-50	7
50-60	3
60-70	2
70-80	2
80-90	3
90-100	9
Total	51

Solution.

Let us first draw a histogram for this data and mark the mid-points of the rectangles' tops as B, C, D, E, F, G, H, I, J, K, respectively. The point where this line segment meets the vertical axis is marked as A. Let L be the mid-point of the class succeeding the last class of the given data. The OABCDEFGHIJKL is the frequency polygon, which is shown.

2. In a city, the weekly observations made in a study on the cost of living index are given in the following table. Find the class-marks for all the classes.

Cost of living index	Number of weeks
140-150	5
150-160	10
160-170	20
170-180	9
180-190	6
190-200	2
Total	52

Solution.

Let us find the class-marks of the classes given above, that is of 140 - 150, 150 - 160,... For 140 - 150, the upper limit = 150, and the lower limit = 140.
So, the class-mark = 150+140/2= 290/2= 145.

Continuing in the same manner, we find the class-marks of the other classes as well.

The table is as follows:

Classes	Class-marks	Frequency
140-150	145	5
150-160	155	10
160-170	165	20
170-180	175	9
180-190	185	6
190-200	195	2
Total		52

3. Draw a frequency polygon for the data above (without constructing a histogram).

Solution.

We can now draw a frequency polygon by plotting the class-marks along the horizontal axis, the frequencies along the vertical axis, and then plotting and joining the points. So, the resultant frequency polygon will be ABCDEFGH.

Image Source: NCERT

FAQs on frequency polygon

Let us take a look at the frequently asked questions related to frequency polygons:

Commonly asked questions

What are the advantages of frequency polygons?

The following points highlight the importance of frequency polygons:

Frequency polygons are useful for comparing distributions of multiple datasets on the same graph. It becomes easy to visually compare shapes and trends of different datasets by overlaying multiple frequency polygons.
These use lines to connect points which provide a continous representation of the data. It is easier to see patterns and trends over intervals through frequency polygons.
They can simplify the visualization of complex data which makes it easy to interpret the overshap and data distribution without distraction of bins or bars.
Line format of frequency polygon help in identifying trends, patterns and changes in data over time. This is especially useful in time series analysis.
Frequency polygons visualize measures of central tendency and spread by providing clear view of data distribution.
These can be used with different types of data and they are not limited by either number of bins of width of intervals. This makes it a flexible tool for data analysis tasks.

How many types of frequency polygons are there?

The following are different types of frequency polygons:

Simple Frequency Polygon: This is a standard form that connects the midpoints of tops of the bars in a histogram with straight lines.
Relative Frequency Polygon: This type of frequency polygon uses relative frequencies (proportions or percentages) instead of using absolute frequencies. This frequency polygon is used for comparing datasets of different sizes.
Cumulative Frequency Polygon (Ogives): Ogives are related and they represent cumulative frequencies. These can be used for showing the cumulative distribution of data and are used with frequency polygons.
Smoothed Frequency Polygon: Rather than connecting points with straight lines, smoothed curves or splines might are used to give a more continuous appearance to data distribution.
Overlayed Frequency Polygons: Multiple frequency polygons can be overlaid on same graph for comparing different datasets or distributions.

How to work out probability from a frequency polygon?

Since a frequency polygon represents the data distribution, by interpreting the areas under curve, it is possible to infer probabilities for some range and interval. Let us take a look at it:

Understanding the Data: You must be able to comprehend the data represented by frequency polygon. In most cases, x-axis represents data values/intervals and y-axis represents frequency or relative frequency of those values.
Conversion to relative frequency: If frequency polygon is based on absolute frequencies, first convert it into relative frequency by dividing every frequency by total number of observations.
Identifying the area of interest: Then you need to determine the range or interval for which you need to find the probabolity. This might be a specific bin or a range of values on x-axis.
Estimate area under curve: To find the probability of specific range, you need to estimate area under curve for that range. This is possible by approximating area using geometric shapes such as trapezoids and rectangles.