Frequency Polygons in Statistics

Frequency Polygons in Statistics: A frequency polygon is a type of line graph where the frequencies of classes are plotted against their midpoints. This graphical representation closely resembles a histogram and is typically used for comparing data sets or showing cumulative frequency distributions. It uses a line graph to represent quantitative data.

Frequency polygons are one of the great methods to represent statistical data so that it can be read easily. In statistics, we deal with lots of data, and reading it quickly is necessary for solving statistical problems effectively.

Frequency polygons help us to achieve the same result. In this article, we will learn about frequency polygons, their formula, examples, and others in detail.

Frequency Polygons

What is a Frequency Polygon in Statistics?

A visual representation of the frequency distribution of continuous data is the frequency polygon. Karl Pearson, an English statistician, made the initial presentation of it in the late 19th century. Based on the research of earlier statisticians like Francis Galton and Adolphe Quetelet, he put forth the idea. Its value comes from its capacity to graphically portray data, making understanding and analysis easier. They, therefore, serve as an important tool in statistics, assisting researchers in finding patterns and trends in huge data sets.

They are useful for showing data sets with numerous observations or values, which is one of their key features. The polygon represents the data distribution succinctly and clearly by splitting the data into equal intervals and charting the frequency of each container. As they take the shape of points that sit beyond the typical range of the distribution, they are also useful in finding outliers or abnormalities in the data set. Once more, this facilitates identifying and examining odd or unexpected data points.

Frequency Polygon Definition

Frequency polygons are a type of graphical data distribution that aids in recognizing the data by giving it a particular form. Although frequency polygons and histograms are quite similar, they are more effective when comparing two or more sets of data. As a line graph, the graph primarily shows data from the cumulative frequency distribution.

Formula to Find Midpoint of Frequency Polygons

If you want to plot a frequency polygon graph, you must figure out the midpoint or class mark for each of the class intervals. The following is the formula to achieve that:

Class Mark (Midpoint) = (Upper Limit + Lower Limit) / 2

Frequency Polygon Graph

Frequency Polygon Graph is the graphical representation of the data given in the form of class interval and frequency. Let’s consider an example for better understanding:

Example: Plot the graph of the Frequency Polygon for the following data which represents the number of goals scored in a match in a league throughout the season:

Goals Scored	Frequency
0	3
1	7
2	8
3	12
4	2
5	5

Answer:

For the given data, we can plot the frequency polygon by representing the goals scored on the vertical axis and frequency on the horizontal axis, as follows:

Cumulative Frequency Polygon

In statistics, the cumulative frequencies of a dataset are shown graphically using cumulative frequency polygons. The dots at the upper-class borders are plotted against the corresponding cumulative frequencies to create the graph. The graph illustrates the visual accumulation of data across time or intervals. The polygon created by the line connecting the points aids in the visualization of the data’s trends and patterns.

It helps analysts grasp the structure and central tendency of cumulative frequency distributions by clearly showing them. Researchers and analysts may get important insights into the distribution of the data and make wise judgments based on the trends seen by employing cumulative frequency polygons.

How to Draw Frequency Polygon?

Following the procedures listed below, construct a histogram before beginning to draw frequency polygons:

• Step 1: First, select the class interval and then indicate the values on the axes.
• Step 2: Label the horizontal axes with the midpoint of each interval.
• Step 3: Label the vertical axes with the class frequency.
• Step 4: Mark a point at the height in the centre of each class interval according to the frequency of each class interval.
• Step 5: Use the line segment to join these spots.
• Step 6: The representation that was obtained is a frequency polygon.

Read More: Bar Graphs and Histograms

Histogram and Frequency Polygons

The difference between the frequency polygon and histogram is discussed in the table below:

Frequency Polygons	Histogram
A frequency polygon graph allows for more visually accurate data comparison.	In a histogram graph, data comparison is not visually pleasing.
The midpoint of the frequencies is utilized in a frequency polygon graph.	The frequencies in a histogram are uniformly distributed throughout the class intervals.
The data of a certain class interval is represented by the correct points in a frequency polygon graph.	The height of the bars in a histogram simply represents the amount of data.
A line segment used to represent a curve is called a frequency polygon graph.	A histogram is a graph that presents data as a series of uninterrupted, rectangular bars.

Frequency Polygons Examples

Example 1: The frequency data below was used to create a frequency polygon.

Class Interval	Frequency
49.5-59.5	5
59.5-69.5	10
69.5-79.5	30
79.5-89.5	40
89.5-99.5	15

Solution:

By first determining the classmark using the equation Classmark = (Upper Limit + Lower Limit) / 2, we may build a frequency polygon without a histogram. Additionally, by combining the previous and next frequencies, we can get the cumulative frequency of each class interval.

Class Interval:

• (59.5 + 49.5/2) = 54.5
• (69.5 + 59.5/2) = 64.5
• (79.5 + 69.5/2) = 74.5
• (89.5 + 79.5/2) = 84.5
• (99.5 + 89.5/2) = 94.5

Class Interval	Lower Bound	Upper Bound	Classmark	Frequency
49.5-59.5	49.5	59.5	54.5	5
59.5-69.5	59.5	69.5	64.5	10
69.5-79.5	69.5	79.5	74.5	30
79.5-89.5	79.5	89.5	84.5	40
89.5-99.5	89.5	99.5	94.5	15

We note the before and after classmarks as well while plotting the graph. The before in this instance is 44.5, while the after is 104.5. The scores are shown on the x-axis, while the frequency is indicated on the y-axis. Consequently, the frequency polygons graph will seem like follows:

Example 2: Assume that a class of 65 students’ weights are distributed as follows: 15 – 25, 25 – 35, 35 – 45, and 45 – 55. How many grade points would there be for each weight category?

Solution:

Formula used to get the classmark for a Frequency Polygon Graph is:

Classmark = (Upper Limit + Lower Limit) / 2

Hence,

• Class interval 15-25 = (15 + 25)/2 = 20
• Class interval 25-35 = (25 + 35)/2 = 30
• Class interval 35-45 = (35 + 45)/2 = 40
• Class interval 45-55 = (45 + 55)/2 = 50

Frequency Polygons Are Used For – Applications

Here are some of the key applications of frequency polygons:

1. Comparing Distributions: Frequency polygons allow for easy comparison between different datasets. By overlaying multiple polygons on the same graph, you can visually assess differences in shapes, spreads, and central tendencies of the distributions.
2. Identifying Skewness and Kurtosis: The shape of a frequency polygon can provide insights into the skewness (asymmetry) and kurtosis (peakedness) of the data distribution. This is useful for understanding the nature of the dataset, whether it is normally distributed, positively skewed, negatively skewed, etc.
3. Analyzing Trends: In time series data, frequency polygons can help in visualizing trends over time. This makes it easier to identify patterns such as seasonal variations or cyclic changes.
4. Educational Tool: In teaching statistics, frequency polygons serve as a clearer alternative to histograms for some students. They can help in understanding how frequencies change between intervals.
5. Cumulative Frequency Analysis: Although not a cumulative frequency graph itself, frequency polygons can be adapted to show cumulative frequencies, providing a visual representation of data accumulation over intervals.

People Also View:

• How to Make a Frequency Polygon in Excel?
• Frequency Distribution – Definition, Types, Table, Graph
• Types of Polygons

Summary – Frequency Polygons in Statistics

Frequency polygons are graphical tools used in statistics to represent the distribution of data points. They are essentially line graphs that plot class frequencies against class midpoints, making them very similar to histograms but offering a clearer visual comparison between multiple datasets. These graphs are particularly valuable for analyzing trends, comparing distributions, and identifying characteristics such as skewness and kurtosis in the data. By providing a visual summary of data, frequency polygons serve as an effective educational tool to enhance understanding of statistical distributions and are useful in diverse applications from business analytics to academic research.

FAQs on Frequency Polygons in Statistics

What is Frequency Polygon?

Frequency Polygon is a way of representing continuous data in statistics and is similar to Histogram in statistics.

What Kind of Data is Appropriate for a Frequency Polygon?

Frequency Polygons are suitable for continuous data like height, weight, temperature, or time. They can, however, be used for discrete data that is classified into intervals, such as test scores or income bands.

Why Are Frequency Polygons Used?

Frequency polygon graphs are used to compare a group of data because they are more clear and legible. These graphs are also commonly used to represent the cumulative frequency distribution.

What are the Features of Frequency Polygons?

A frequency polygon graph is a closed dimensional diagram consisting of a line segment connecting the midpoints of the supplied class intervals. The graph can be made either with or without a histogram. The first point lies on the x-axis at y = 0, in the midst of the interval before the first class interval.

What is the Difference Between a Frequency Polygon and a Frequency Curve?

The main distinction between a frequency polygon and a frequency curve is that a frequency polygon is drawn by combining points with a straight line, but a frequency curve is drawn with a smooth hand.

Are Frequency Polygon and Histogram the Same?

No, it is not comparable, however it does have certain characteristics. The main distinction between both is that a histogram is a graphical representation of data made up of contiguous rectangles, whereas a frequency polygon is a curve made up of the midpoints of those rectangles.