What are Frequency Polygons? - Definition and Advantages
Grouping of data is made easy by the use of frequency polygons:
When we are working on a particular thing, it is necessary to make sure that we record all the data that we have. This is going to be useful for the following reasons:
1. The data is going to be preserved and others who need it can use it at a later stage.
2. It is going to act as a check for the ones working on it to compare and contrast all the possible entries.
Hence, recording all the data is very much important as such. There are many types in which one can choose to represent the data. Here are a few of the forms:
1. Pictorial Representation: It is a general belief that people will remember things in the form of pictures very easily. Therefore, people have decided to represent the data in the form of pictures. This is one of the best methods but the major disadvantage is that pictures are going to consume a lot of time and the entire idea is going to take a lot of effort.
2. Sheets: This representation of data wherever possible is one the best methods as the data can be retrieved easily. There is one major drawback with this form. All the data is in a clustered form and it is very difficult for the people to see to it that they are going to segregate the data.
3. Graphical Representation: This is found to be one of the best forms of representation of data. This is used widely by many people all over the world. This is one the most efficient methods of representation as such.
Frequency Polygons
Frequency polygons are one type of graphical representation of data. There are many ways in which the data can be graphically represented and frequency polygons are the best and the most efficient of all.
The data that is present on a sheet of paper in the form of tables is sorted out and made in such a way that it can be plotted on a graph paper. This is going to be very much useful for the people who are reading the data. The graph so plotted is also represented in the form of bars so that it is clearer for the people to understand the statistics as such.
All this helps to understand the frequency distribution of the data in a much better way.
What are the advantages of Frequency Polygons?
1. The frequency polygons not only help to make sure that the data is sorted out and represented, but they are also going to make it easier for the people to compare and contrast all the results.
2. These are much easier to understand and they give a clear picture of the distribution of data. It is necessary that people should be able to read these graphs to understand them as such.
3. This method is not even time taking like a few other processes. If the techniques that are used to draw and represent the data are known, this becomes easier as such.
Terms associated with Frequency Polygons:
1. Class Interval: It is necessary that the people should select a proper class interval. Class interval is nothing but a specific range in which the data is going to fall. This should make the data appear simple and easy.
2. Midpoint: This is the center point of the bar is to be drawn for the data and this should be identified for the symmetry of the graph as such.
3. Class Mark: It is nothing but the midpoint. It is the mean of the upper limit and the lower limit of the class interval.
4. Upper Limit: The upper limit is the ending boundary condition of the class interval.
5. Lower Limit: The lower limit is the starting boundary condition of the class interval.
How to Draw a Frequency Polygon?
1. Select a suitable class interval for the entire data that is available. Usually, the class interval is plotted on the X-axis or the horizontal line and the frequencies that are corresponding to the class intervals are plotted on the Y-axis or the vertical line.
2. Once the classmark or the midpoint is chosen for all the class intervals, it becomes very easy to plot the graph. The classmark is represented as follows:
Class mark = (U.L + L.L)/2
Where U.L is the upper limit and L.L is the lower limit.
3. It is the choice of the person to either mark the class marks or the class intervals on the horizontal axis. The frequencies are also marked on the vertical axis.
4. There are a few important features to note about the frequency polygons. The height from the horizontal line is always the frequency. It is also important to note that, when the class intervals are being plotted on the X-axis, the midpoint should be considered for the sake of plotting against the frequencies. It should not be plotted against the upper or lower limits. If the class marks are considered directly, then there is nothing to worry about.
5. The obtained points are joined using the lines and this forms the frequency polygon.
6. Considering the height as the frequency and the width as the class intervals, the bars are drawn on the chart to represent the data as such.
Construction of Frequency Polygon with Histogram
First, get the frequency distribution from the given data.
Draw a histogram and join the midpoints of the tops of adjacent rectangles of the histogram with the help of line segments.
Then, get the midpoints of 2 assumed class intervals of zero frequency, one next to the first bar on its left and another next to the last bar on its right. These class intervals are referred to as imagined class intervals.
Now complete the polygon by joining the midpoints of the first and the last class intervals to the midpoint of the imagined class intervals adjacent to them.
Precautions to be Taken While Drawing the Curves:
1. The points should be joined in such a way that they are straight. Freehand curves should be avoided.
2. There are some people who skip out on drawing rectangles. It is necessary that they should make it a point to draw them because these are going to provide a wider picture of the data that is being represented on the graph.
These frequency distributions have been a great way to group and organize the data. It would be great if the people make sure that they know how to read all these graphs for that matter.
Use of Frequency Polygons
The frequency polygons are used in the following cases and situations: (i) When the data is large, extensive, and continuous in form, and (ii) for comparing the two different sets of data having the same nature.
Important points
The following things are needed to be kept in mind while drawing a frequency polygon:
While drawing frequency polygons, joining points should be in a straight manner
Be sure to avoid free-hand curves, and skip drawing rectangles
Frequency polygons provide a clear picture of the data that is being represented on the graph.
A frequency polygon is one of the easiest ways for grouping the data. It is a visual way of presenting quantitative data and its frequency.
It is used to compare data sets or represent a cumulative frequency distribution. The formula for calculating Classmark for each interval is -
FAQs on Frequency Polygons
1. What are frequency polygons?
A frequency polygon is defined as a line graph created by joining all of the top points of a histogram. They are called polygons because the line the graph creates resembles half of a polygon.
Frequency polygons illustrate the shape of a distribution of data
Frequency polygons can be seen with or without the histogram bars
They have endpoints that lie on the x-axis
They can be used to compare two sets of data
Frequency polygons are perfect for comparisons of data having the same sample size
2. What are the steps to draw a frequency polygon?
The steps to draw frequency polygons are mentioned below:
First, mark the class interval values on the horizontal axis.
Then, mark frequencies correspond to the class interval on the vertical axis but not on the upper or lower limit.
Now mark the mid-value on the horizontal axis, and mark the frequency of the class intervals.
Then, join all the points and make a line segment.
The curve formed is called a frequency polygon.
