Frequency Polygon – Concept, Steps, Solved Questions & Uses

The concept of frequency polygon plays a key role in mathematics and is widely used in statistics to represent data visually for both classroom learning and exams. Understanding frequency polygons makes interpreting, comparing, and analyzing grouped data much easier for students.

What Is Frequency Polygon?

A frequency polygon is a special type of line graph that shows the distribution of frequency for a set of grouped or ungrouped data by joining points at the class mid-values with straight lines. You’ll find this concept applied in areas such as statistics, graphical data representation, and even in competitive exam data analysis.

Key Formula for Frequency Polygon

Here’s the standard formula for finding the class mark (midpoint), which you use when plotting a frequency polygon:
\( \text{Class Mark} = \frac{\text{Upper Limit} + \text{Lower Limit}}{2} \)

Cross-Disciplinary Usage

Frequency polygons are useful in Maths, but also play an important role in Physics, Computer Science, Economics, and social sciences. For students preparing for board exams or Olympiads, visualizing data using frequency polygons helps in data-driven reasoning and quick pattern recognition. You might encounter questions involving frequency polygons in exams like CBSE, ICSE, and IGCSE as well.

Step-by-Step Illustration

1. Prepare the frequency distribution table.
   
   List class intervals and corresponding frequencies. Example:

   Class Interval	Frequency
   10–20	5
   20–30	8
   30–40	12
   40–50	7

   
   
2. Find the class marks for each interval.
   
   Calculate class marks:
   10–20: (10+20)/2 = 15
   20–30: (20+30)/2 = 25
   30–40: (30+40)/2 = 35
   40–50: (40+50)/2 = 45
   
   
   
3. Plot the class marks (x-axis) against frequencies (y-axis).
   
   On graph paper, label the x-axis as "class mark" and y-axis as "frequency." Then, plot the points: (15,5), (25,8), (35,12), (45,7).
   
   
4. Anchor the polygon at the baseline.
   
   Add one class mark before the first and after the last interval with frequency zero, i.e., (5,0) and (55,0), to make the polygon closed at both ends.
   
   
5. Join the points with straight lines.
   
   Connect all these points in order using straight lines to complete your frequency polygon.

Speed Trick for Frequency Polygon Drawing

Many students get confused between histograms and frequency polygons. Here’s a quick guide to avoid mistakes and draw a frequency polygon efficiently:

1. Don’t draw bars — just plot the midpoints of each class interval directly.
2. Always use the class mark, not just class boundaries, for plotting.
3. Start and end your polygon at the baseline for clear enclosure.

Tip: When two data sets have the same class intervals, you can plot frequency polygons for both in the same graph and easily compare their shapes, peaks (modes), and spreads.

Example Problem: Constructing a Frequency Polygon

Let’s solve a common board-style question:

Question: The marks scored by 30 students in a test are grouped as shown below. Draw the frequency polygon.

Marks	No. of Students
0–10	4
10–20	7
20–30	12
30–40	5
40–50	2

Solution Steps:

1. Find class marks:

0–10: (0+10)/2 = 5
10–20: (10+20)/2 = 15
20–30: (20+30)/2 = 25
30–40: (30+40)/2 = 35
40–50: (40+50)/2 = 45

2. Plot the points (marks, frequency):

(5,4), (15,7), (25,12), (35,5), (45,2).

3. Add extra points at both ends:

Add (–5,0) before and (55,0) after to anchor.

4. Join points in order by straight lines.

Your frequency polygon is complete.

Types and Features of Frequency Polygon

Type	Feature
Simple Frequency Polygon	Created from a single frequency distribution
Cumulative Frequency Polygon (Ogive)	Plots cumulative frequency (increasing total)
Multiple Frequency Polygons	Compare two or more data sets on the same graph

• Shows the shape and spread of data clearly.
• Helps to compare distributions visually.
• The peak point shows the mode (most frequent value).

Advantages and Disadvantages

Advantages	Disadvantages
Easy comparison Visualizes large datasets Identifies mode and trends	Approximate for small datasets Less precise than bar graphs for exact values Needs careful plotting of midpoints

Try These Yourself

• Draw a frequency polygon for the data: 5, 8, 12, 7 (class intervals: 10–20, 20–30, 30–40, 40–50).
• Given class intervals 0–5, 5–10, 10–15 with frequencies 2, 6, 7, find and plot their mid-values.
• Compare a frequency polygon with a histogram for the same data. What differences do you see?
• Find the mode from a drawn frequency polygon curve.

Frequent Errors and Misunderstandings

• Plotting frequencies at upper or lower limits instead of class marks.
• Forgetting to anchor the polygon ends at frequency zero.
• Confusing frequency polygons with line graphs or histograms.
• Not using equal class intervals – this makes the polygon misleading.

Relation to Other Concepts

The idea of frequency polygon is closely connected with histogram, cumulative frequency distribution (ogive), and line graph. Mastering frequency polygons helps in understanding the broader topic of representing and interpreting statistical data.

Classroom Tip

A simple way to remember frequency polygons: "Midpoints meet, lines connect, ends touch baseline." Vedantu’s teachers regularly explain this using colorful class activities so students can visualize the concept better.

We explored frequency polygons—from the definition, formula, step-by-step construction, examples, common mistakes, and their connection to other data representations. Continue practicing with Vedantu to become confident in using frequency polygons for any exam or real-life data comparison.

Explore more about: Histogram, Cumulative Frequency Distribution, Line Graph, Statistics.