A frequency polygon is almost identical to a histogram, which is used to compare sets of data or to display a cumulative frequency distribution. It uses a line graph to represent quantitative data.
Statistics deals with the collection of data and information for a particular purpose. The tabulation of each run for each ball in cricket gives the statistics of the game. Tables, graphs, pie-charts, bar graphs, histograms, polygons etc. are used to represent statistical data pictorially.
Frequency polygons are a visually substantial method of representing quantitative data and its frequencies. Let us discuss how to represent a frequency polygon.
Steps to Draw Frequency Polygon
To draw frequency polygons, first we need to draw histogram and then follow the below steps:
- Step 1- Choose the class interval and mark the values on the horizontal axes
- Step 2- Mark the mid value of each interval on the horizontal axes.
- Step 3- Mark the frequency of the class on the vertical axes.
- Step 4- Corresponding to the frequency of each class interval, mark a point at the height in the middle of the class interval
- Step 5- Connect these points using the line segment.
- Step 6- The obtained representation is a frequency polygon.
Let us consider an example to understand this in a better way.
Example
Example 1: In a batch of 400 students, the height of students is given in the following table. Represent it through a frequency polygon.
Solution:Following steps are to be followed to construct a histogram from the given data:
- The heights are represented on the horizontal axes on a suitable scale as shown.
- The number of students is represented on the vertical axes on a suitable scale as shown.
- Now rectangular bars of widths equal to the class- size and the length of the bars corresponding to a frequency of the class interval is drawn.
ABCDEF represents the given data graphically in form of frequency polygon as:
Frequency polygons can also be drawn independently without drawing histograms. For this, the midpoints of the class intervals known as class marks are used to plot the points.
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FAQs
Step 1: Choose your class interval - the size of each class or bin that the data is divided into. Step 2: Label the -axis with the midpoints of each class. Label the -axis with frequencies. Step 3: Place a point corresponding to each class and its frequency.
What is a frequency polygon with examples? ›
A frequency polygon is a type of line graph where the class frequency is plotted against the class midpoint and the points are joined by a line segment creating a curve. The curve can be drawn with and without a histogram. A frequency polygon graph helps in depicting the highs and lows of frequency distribution data.
What are the parts of a frequency polygon? ›
The frequency polygon is a curve that is drawn on the x-axis and the y-axis. The x-axis represents the values in the dataset, while the y-axis shows the number of occurrences of each distinct category. The frequency polygon can serve as an alternative to a histogram.
How to draw a frequency curve and polygon? ›
Complete Step by Step Solution:
1) We will plot the histogram for the data values. 2) Then, we will point the midpoints of the class interval on the histogram. 3) Now we will join the midpoints using the straight lines. 4) The graph joined by using straight lines is called frequency polygon.
What is a frequency curve with an example? ›
A frequency curve is a limiting form of a histogram or a frequency polygon. A frequency curve for a given distribution can be obtained by drawing a smooth, free hand curve through the midpoints of the upper sides of the rectangles forming the histogram.
How to find the area of a frequency polygon? ›
The area under the frequency polygon is the same as the area under the histogram and is, therefore, equal to the frequency values that would be displayed in a distribution table. The frequency polygon also shows the shape of the distribution of the data, and in this case, it resembles a bell curve.
How to find mean from frequency polygon? ›
Steps for getting the mean of data when in a grouped frequency table:
- Find each midpoint of the groups and put this as another column.
- Multiply each midpoint by its frequency and write as another column.
- Get the sum of all these values (add them all up).
- Divide this value from step 3 by the total frequency.
Sum the number of points in each interval, divide the sum of each interval by the total number of data points, and multiply by 100. The result is the percentage of the total number of data points that is represented by each interval.
What are the 4 parts of a polygon? ›
The parts of polygons include the sides, interior angles and exterior angles. There is also the vertex, the spot where two sides meet, and the diagonals, or lines connecting vertices.
How to find median from frequency polygon? ›
Remember, when you are working out the median:
- Put the results in numerical order (in a frequency table this will already be done)
- Count the total amount of results and add one.
- Divide this by 2 to find the the position of the middle result.
- Find the middle result in the numerically ordered list or frequency table.
Apart from plotting and joining up points with straight lines there are 2 rules for frequency polygons: Plot points at the MIDPOINT of class intervals. Unless one of the frequencies is 0 do not join the frequency polygon to the x-axis, and do not join the first point to the last one.
What are the steps to prepare frequency polygon? ›
Step 1- Choose the class interval and mark the values on the horizontal axes. Step 2- Mark the mid value of each interval on the horizontal axes. Step 3- Mark the frequency of the class on the vertical axes.
What is a frequency polygon with an example? ›
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.
What are the advantages of frequency polygon? ›
The advantage of using a frequency polygon is that it allows similar sets of data to be plotted on the same graph. Comparisons between the two sets can then be made. For example, this graph shows that there are three more students in Class B with a hand span in the group 20 < h ≤ 22 than in class A.
How to make a frequency graph? ›
First, draw a pair of axes and label them with frequency on the vertical axis (y-axis )and animals on the horizontal axis (x-axis ). Next, use a ruler to draw each bar with the correct height. Draw the heights of the bars depending on its frequency.
How to make a relative frequency polygon? ›
To construct a relative frequency polygon:
Sum the number of points in each interval, divide the sum of each interval by the total number of data points, and multiply by 100. The result is the percentage of the total number of data points that is represented by each interval.
How do you make a frequency polygon continuous? ›
If the classes in a grouped frequency distribution are not continuous, we can make them continuous by finding half of the difference between the upper limit of a class and the lower limit of the next class, and then adding the same to all the lower limits and subtracting it from all the upper limits in the distribution ...
How to make a frequency distribution table? ›
To make such a frequency distribution table, first, write the class intervals in one column. Next, tally the numbers in each category based on the number of times it appears. Finally, write the frequency in the final column. A frequency distribution table drawn above is called a grouped frequency distribution table.
