Understanding Frequency Polygon: Students who are struggling with understanding Frequency Polygon can check out the details here. A graphical representation of data distribution helps understand the data through a specific shape. It is known as frequency polygons. Polygons are like histograms. Frequency polygons help compare two or more data sets. The graph primarily displays data from the cumulative frequency distribution as a line graph. To further comprehend the idea, let’s learn about the frequency polygons graph, the procedures for making a graph, and work through a few examples.

Understanding Frequency Polygons: Definition

It is possible to describe polygons as a type of graph that interprets data or information that is frequently utilised in statistics. This graphic method of data representation aids in accurately and systematically illustrating the data’s shape and trend. Frequency polygons through the graph shape show the number of occurrences of class intervals. Although a histogram is typically used when drawing this kind of graph, it is not required. A frequency polygon graph is a line graph that displays data from a cumulative frequency distribution, whereas a histogram is a graph with rectangular bars and no spaces. 

How to Construct Frequency Polygons?

Check out these steps. It will help understand frequency polygons. On an x-axis and a y-axis, a frequency polygon’s curve is depicted. The y-axis of a regular graph displays the frequency of each category, and the x-axis reflects the value in a dataset. The mid-point, also known as the class interval or class marks, is crucial when plotting a frequency polygon graph. You can draw the frequency polygon curve with or without a histogram. Before creating the frequency polygons for a histogram, we first drew rectangular bars in opposition to the class intervals. The procedures for creating a frequency polygon graph devoid of a histogram are as follows:

Step 1: While plotting the curve on the y-axis, mark the class intervals for each class on the x-axis.

Step 2: Determine the classmarks, which represent the midway of each class interval. 

Step 3: After obtaining the classmarks, mark them on the x-axis.

Step 4: Plot the frequency according to each class mark since the height always represents the frequency. Instead of plotting it on the upper or lower boundary, it should be done against the classmark itself.

Step 5: Following marking the points, connect them with a line segment to create a line graph.

Step 6: The frequency polygon is the curve produced by this line segment.

Understanding Frequency Polygon: How to Find the Midpoint of Frequency Polygons

We must determine the midpoint or classmark for each class interval while plotting a frequency polygon graph. The method is as follows:

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

Difference Between Histogram and Frequency Polygons

Despite the fact that a frequency polygon graph and a histogram can both be produced, the two graphs are still distinct from one another. The differences between the two graphs may be seen thanks to each of their distinct features visually. The distinctions are:

Frequency Polygons	Histograms
A frequency polygon graph is a curve depicted by a line segment.	A histogram is a graph, and it shows data through rectangular-shaped bars without any spaces between them.
We use the midpoint of the frequencies in a frequency polygon graph.	The frequencies are uniformly distributed over the class intervals in a histogram.
A frequency polygon graph’s precise points indicate the data for a given class interval.	The bars’ height in a histogram depicts the data quantity.
Data comparison is visually more correct in a frequency polygon graph.	Data comparison is not visually appealing in a histogram graph.

Check out the below examples. Understanding Frequency Polygon will become easy for you.

Example 1: Let us check out how to construct a frequency polygon using the data given below without a histogram.

Test Scores	Frequency
79.5 to 89.5	15
69.5 to 79.5	7
59.5 to 69.5	3
49.5 to 59.5	10

Solution:

Using the equation Classmark = (Upper Limit + Lower Limit) / 2, we may first determine the classmark before building a frequency polygon without a histogram. By combining the subsequent frequency and previous frequency, we can also determine the cumulative frequency for 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

Test Scores	Frequency	Classmark
89.5 to 99.5	15	94.5
79.5 to 89.5	10	84.5
69.5 to 79.5	7	74.5
59.5 to 69.5	5	64.5
49.5 to 59.5	3	54.5

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

Example 2: The following table lists the weekly observations made in research on the cost of living index in a city: For the information below, make a frequency polygon using a histogram.

Cost of Living Index	Number of weeks
190 to 200	6
180 to 190	10
170 to 180	20
160 to 170	14
150 to 160	8
140 to 150	2
Total	60

The following procedures must be taken to create a histogram to plot a frequency polygon with it:

On the x-axis, the cost of living index is displayed.

The y-axis displays the number of weeks.

Now, rectangular bars are drawn with lengths proportional to the frequency of the class interval and widths equal to the size of the class.

Using the equation Classmark = (Upper Limit + Lower Limit) / 2, we can get the midpoint.

Classmark = (160 + 150)/2 = 155 , (150 + 140)/2 = 145, and so on.

Cost of Living Index	Number of weeks	Classmark
190 to 200	6	195
180 to 190	10	185
170 to 180	20	175
160 to 170	14	165
150 to 160	8	155
140 to 150	2	145
Total	60

We note the before and after classmarks as well while plotting the graph. Here, the before value is 135, and the after value is 205. The midpoints of an ABCDEFGH frequency polygon are used to display the given data visually. Consequently, the frequency polygons graph will seem as follows:

Example 3: Assume that a class of 45 students’ weights is distributed as follows: 35 to 45, 45 to 55, 55 to 65, and 65 to 75. What would the grade points be for each weight category?

Solution:

The formula classmark = (Upper Limit + Lower Limit)/2 is used to determine the classmark for a frequency polygon graph.

Hence,

Class interval 35 to 45 is equal to (45 + 35)/2, or 40.

Class interval (55 + 45)/2 = 50 for the range 45-55

Class interval 55 – 65 = (65 + 55)/2 = 60
Class interval 65 – 75 = (75 + 65)/2 = 70

Frequently Asked Questions on Understanding Frequency Polygon

Understanding Frequency Polygon and checking out the frequently asked questions on Frequency Polygon are equally important.

Q.1 What are Frequency Polygons?

Ans: A frequency polygon is a line graph type where the class frequency is plotted against the class midpoint. A line segment joins the points forming a curve. Both a histogram and one without can be used to draw the curve. The highs and lows of frequency distribution data are easier to visualise with a frequency polygon graph. It is necessary to determine the classmark or midpoint from the class intervals in order to derive the curve for a frequency polygon.

Q.2 How are Frequency Polygons Created?

Ans: It is possible to build a frequency polygon both with and without a histogram. Without a histogram, you can create a frequency polygon by following these steps:

We depict the curve on the y-axis while marking the class intervals for each class on an x-axis.

Calculate the classmarks, which are the midway of each class interval.

On the x-axis, place the classmarks.

Plot the frequency according to each class mark since the height represents the frequency in every case. Instead of plotting it on the upper or lower boundary, it should be done against the classmark itself.

Mark all of the points, then connect them with a line segment to create a line graph.

This line segment produces a curve that represents the frequency polygons.

Q.3 What distinguishes frequency polygons from histograms?

Ans: A frequency polygon graph is a histogram that has been improved. A frequency polygon is a line graph where a curved line shows the data, whereas a histogram is a bar graph with rectangle-shaped bars representing the data. When comparing distributive data, frequency polygons are more frequently employed because a histogram would make the comparison unclear.

Q.4 Why are Frequency Polygons used?

Ans: Frequency polygon graphs are used to compare sets of data because they are more readable and transparent. Cumulative frequency distribution is frequently represented using these graphs as well.

Q.5 What traits do frequency polygons possess?

Ans: A closed-dimensional figure of a line segment connecting the midpoints of the specified class intervals is referred to as a frequency polygon graph. Either a histogram or no histogram can be used to draw the graph. The initial point, where y = 0, is situated in the middle of the interval before the first class interval on the x-axis.

Q.6 What is the relationship between Line Graphs and Frequency Polygons?

Ans: The midpoints of all the class intervals are connected to form a frequency polygon, a type of line graph. The curved line’s form aids in presenting precise data. Frequency polygon graphs and line graphs are both frequently utilised when data is required to be compared.

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