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Frequency table Grouped frequency table Coordinate plane Plot points on a graphFrequency polygon
Here you will learn about frequency polygons, including what they are and how to construct them.
Students will first learn about frequency polygons as part of statistics and probability in high school.
What is a frequency polygon?
A frequency polygon is a graph that shows the frequencies of grouped data. It is a type of frequency diagram that plots the midpoints of the class intervals against the frequencies and then joins up the points with straight lines.
Frequency polygons are used to display a set of data and show the frequency distribution over a continuous scale.
To construct a frequency polygon, you need to know the value for the frequency of each group.
For example,
Below is an example of a frequency polygon, with the associated frequency distribution table.
The grouped data is presented as a continuous scale on the horizontal axis – you do not show the exact class intervals on the graph.
What is a frequency polygon?
Common Core State Standards
How does this relate to high school math?
- High School – Statistics & Probability – Interpreting Categorical & Quantitative Data (HS.S.ID.B.5)
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
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DOWNLOAD FREEHow to draw a frequency polygon
In order to draw a frequency polygon:
- Calculate the midpoint of each class interval.
- Plot the class frequency at the midpoint for the class.
- Connect the plotted values using straight line segments.
Frequency polygon examples
Example 1: standard problem
The lengths L{~cm} of 16 carrots were measured and recorded in a grouped frequency table.
Draw a frequency polygon to represent the grouped data. Use the horizontal and vertical axes below.
- Calculate the midpoint of each class interval.
The midpoints can be found by adding the lower limit of the class interval to the upper limit of the class interval and dividing by 2.
2Plot the class frequency at the midpoint for the class.
The midpoints are the x- coordinate and the frequencies are the y- coordinate.
3Connect the plotted values using straight line segments.
Join the first point to the second point with a straight line. Keep joining the points in order with straight lines.
Example 2: large class intervals
18 students were asked to hop on one leg as far as they could in 3 minutes. The results were grouped in the table below.
Draw a frequency polygon on the axes provided to represent this data.
Calculate the midpoint of each class interval.
The midpoints can be found by adding the lower limit of the class interval to the upper limit of the class interval and dividing by 2.
Plot the class frequency at the midpoint for the class.
The midpoints are the x- coordinate and the frequencies are the y- coordinate.
Connect the plotted values using straight line segments.
Join the first point to the second point with a straight line. Keep joining the points in order with straight lines.
Example 3: standard problem
Draw a frequency polygon for the following grouped data on the axes provided showing the average speed of vehicles traveling down a road.
Calculate the midpoint of each class interval.
The midpoints can be found by adding the lower limit of the class interval to the upper limit of the class interval and dividing by 2.
Plot the class frequency at the midpoint for the class.
The midpoints are the x- coordinate and the frequencies are the y- coordinate.
Connect the plotted values using straight line segments.
Join the first point to the second point with a straight line. Keep joining the points in order with straight lines.
Example 4: worded problem
An electrician is measuring the output voltage of plug sockets. He collects the data points into groups shown in the table below.
Draw a frequency polygon to represent the data on the set of axes below.
Calculate the midpoint of each class interval.
The midpoints can be found by adding the lower limit of the class interval to the upper limit of the class interval and dividing by 2.
Plot the class frequency at the midpoint for the class.
The midpoints are the x- coordinate and the frequencies are the y- coordinate.
Connect the plotted values using straight line segments.
Join the first point to the second point with a straight line. Keep joining the points in order with straight lines.
Example 5: standard problem – 5 rows
Data for the test score as a percentage is given in the table below.
Use the set of axes below to draw a frequency polygon for the data. Label each axis.
Calculate the midpoint of each class interval.
The midpoints can be found by adding the lower limit of the class interval to the upper limit of the class interval and dividing by 2.
Plot the class frequency at the midpoint for the class.
The midpoints are the x- coordinate and the frequencies are the y- coordinate.
Don’t forget to label the x- axis and y- axis titles.
Connect the plotted values using straight line segments.
Join the first point to the second point with a straight line. Keep joining the points in order with straight lines.
Example 6: different class intervals
The time T seconds for a raft of penguins to dive into water from a ledge was recorded in a grouped frequency table below.
Draw a frequency polygon on the axes below for the following grouped data.
Calculate the midpoint of each class interval.
The midpoints can be found by adding the lower limit of the class interval to the upper limit of the class interval and dividing by 2.
Plot the class frequency at the midpoint for the class.
The midpoints are the x- coordinate and the frequencies are the y- coordinate.
Connect the plotted values using straight line segments.
Join the first point to the second point with a straight line. Keep joining the points in order with straight lines.
Teaching tips for frequency polygon
- Briefly review key features of bar graphs (individual bars for each category), line graphs (show changes over time by connecting points), and pie charts (represent proportions of a whole).
- Overlay a frequency polygon on a frequency histogram of the same data. This helps students see how both display the same information, but the frequency polygon smooths the shape of the data, meaning trends are easier to identify.
- When teaching about frequency polygons, emphasize that they are a valuable tool in descriptive statistics. Explain that descriptive statistics involves summarizing and presenting data in a clear way, and frequency polygons help visually describe the distribution of a dataset.
- Show students how to make a frequency polygon in Excel to help them visualize data distribution and trends.
Easy mistakes to make
- Joining all of the points
Do not join the last point to the first point.
- Using the endpoints, not the midpoints
The coordinate must be plotted at the center of each class interval, at the given frequency.
- Writing frequencies as non-whole numbers
Since frequencies are a count of how many times an item occurs, they will always be integers. They are not decimals. The midpoint can be a decimal.
- Drawing curved lines
The coordinates of a frequency polygon are joined using a straight line segment. Do not connect them using freehand or draw them curved like a cumulative frequency curve; they should be drawn using a ruler.
- Drawing the wrong type of graph
A frequency polygon is a specific type of frequency diagram. Do not draw a bar chart or a vertical line diagram – they are not distinctly frequency polygons.
Related frequency graph lessons
Practice frequency polygon questions
1. Which is the correct frequency polygon for the given data?
Plotting the coordinates and joining them with straight line segments, you get:
2. Which is the correct frequency polygon for the following data?
Plotting the coordinates and connecting them using straight line segments, you get:
3. Which is the correct frequency polygon for the grouped frequency table?
These coordinates need joining up with straight line segments to achieve the solution:
4. Which is the correct frequency polygon for the grouped frequency table?
These coordinates need joining up with straight line segments to get the solution:
5. Which is the correct frequency polygon for the grouped frequency table?
Each coordinate is to be plotted and connected with a straight line segment to the next coordinate:
6. Which is the correct frequency polygon for the grouped frequency table?
These need joining up with straight line segments to get the solution:
Frequency polygon FAQs
A frequency polygon is a type of graph that displays the distribution of data. It is created by plotting points at the midpoints of intervals on a frequency table, with each point representing the frequency of each class, and connecting the points with straight lines.
To draw a frequency polygon, create a frequency table by organizing your data into intervals and listing the corresponding frequencies.
Next, calculate the midpoints of each interval and plot points at these midpoints with their corresponding frequencies.
Finally, connect the plotted points with straight lines.
Frequency polygons are similar to histograms because both serve as graphical representations that display data frequencies across intervals.
While histograms use bars for each class, frequency polygons connect points at the midpoints of these intervals.
Both illustrate the shape of the cumulative frequency distribution, allowing for visual comparisons of data accumulation over time.
A frequency polygon displays the frequency of each class by plotting points at the midpoints of intervals and connecting them with straight lines, showing the distribution of data.
An ogive graph plots cumulative frequencies and shows how the data accumulates over intervals, giving a visual of the total frequency up to each class.
The next lessons are
- Types of sampling
- Probability
- Compound events
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