FREQUENCY POLYGON
Definition Of Frequency Polygon
In a Frequency Polygon, a line graph is drawn by joining all the midpoints of the top of the bars of a histogram.
More About Frequency Polygon
A frequency polygon gives the idea about the shape of the data distribution.
The two end points of a frequency polygon always lie on the x-axis.
Video Examples: Frequency diagrams/polygons
Example of Frequency Polygon
The frequency polygon shown above represents the number of vehicles that passes through a particular route in different hours. To draw the above diagram first a histogram is drawn and then a line graph is drawn through the midpoints of the top of the bars.
Solved Example on Frequency Polygon
Ques: The number of hours each student of a class spends for studying are 5, 8, 7, 6, 8, 8, 5, 5, 6, 5, 6, and 5 hours. Identify the frequency polygon for the given data.
Choices:
A. Figure 1
B. Figure 2
C. Figure 3
D. Figure 4
Correct Answer: A
Solution:
Step 1: The heights of the bars in the histograms indicate the number of hours that the students of a class spend.
Step 2: Observe the heights of the bars in the histograms to match with the given values.
Step 3: Compute the midpoints of the bars and draw the lines along these midpoints.
Step 4: Frequency polygon of this data will be as follows.
Step 5: So, Figure 1 represents the frequency polygon for the given data.
Quick Summary
- A frequency polygon is a line graph derived from a histogram.
- It connects the midpoints of the tops of the histogram bars.
- It illustrates the distribution of data.
- The endpoints of a frequency polygon always lie on the x-axis.
🍎 Teacher Insights
Emphasize the connection between histograms and frequency polygons. Use real-world examples of data to illustrate the creation and interpretation of frequency polygons. Encourage students to compare the shapes of different frequency polygons and discuss what they reveal about the underlying data.🎓 Prerequisites
- Histograms
- Bar Graphs
- Data Representation
- Coordinate Plane
Check Your Knowledge
Q1: What does a frequency polygon represent?
Q2: Which of the following is NOT a characteristic of a frequency polygon?
Q3: Which of the following is the first step to drawing a frequency polygon?
Frequently Asked Questions
Q: What is the purpose of a frequency polygon?
A: It provides a clear visualization of the shape and distribution of a dataset, making it easy to identify trends and patterns.
Q: How do you create a frequency polygon?
A: First, create a histogram. Then, find the midpoint of the top of each bar and connect these midpoints with straight lines. Ensure the polygon starts and ends on the x-axis.
Q: How does a frequency polygon relate to a histogram?
A: A frequency polygon is derived from a histogram by connecting the midpoints of the bars. Both represent the frequency distribution of data, but the polygon emphasizes the shape of the distribution more clearly.