How To Draw A Frequency Polygon
Frequency Polygons
A frequency polygon is a graphical representation of a data fix with frequency data. It is i of the most common statistical tools used to correspond and analyse grouped statistical data.
The use of a frequency polygon has been shown to be very useful for tendency analysis and data recall.
Example of a frequency polygon
Below is an instance of a frequency polygon.
Example of a frequency polygon, Nilabhro Datta - StudySmarter Originals
The value of the data signal is plotted along the horizontal centrality, and the frequency respective to each data point is plotted along the vertical axis. So from the above graph, we can deduce that for x = ten, frequency = viii. Nosotros volition explore further nuances of frequency polygons afterward on.
How to draw a frequency polygon
Given a grouped frequency distribution, follow the following steps to describe the corresponding frequency polygon.
1) Observe the course mark for each grade interval of the frequency distribution. To make information technology easier, you can add some other cavalcade to the frequency distribution to note down the grade marks.
class mark = 
ii) Plot the class marks along the horizontal centrality and the frequencies along the vertical axis.
3) For each course mark, plot the frequency corresponding to that form on the graph.
4) Join all the plotted points in sequential lodge (connect the starting time point with the second, then the second to the third, then on ...)
5) The resulting figure is the necessary frequency polygon.
Example
Draw the frequency polygon graph for the following frequency distribution:
| Course | frequencies |
| 5-7 | 15 |
| 7-9 | 18 |
| 9-11 | 28 |
| 11-13 | vii |
| 13-15 | 22 |
| 15-17 | 35 |
Solutions
First, permit'due south find the class marking for each class. We tin can bear witness the results in the following table:
| Course | Class Marker | frequencies |
| v-7 | half-dozen | xv |
| 7-9 | | 18 |
| 9-11 | ten | 28 |
| xi-13 | 12 | 7 |
| 13-fifteen | 14 | 22 |
| 15-17 | 16 | 35 |
At present that we take all the class marks and the corresponding frequencies, we tin can plot the points on the graph taking the course marks on the horizontal centrality and the frequencies on the vertical axis.
The graph later plotting the requisite points, Nilabhro Datta - StudySmarter originals
Finally, we have to bring together the plotted points sequentially.
The final frequency polygon, Nilabhro Datta - StudySmarter originals
The to a higher place diagram is our final frequency polygon.
Here are a few things to be mindful of when creating your own frequency polygon:
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Brand sure you use the class marking and not the grade limits to plot the graph.
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Sometimes yous may desire to obtain a closed polygon. In such cases, you could extrapolate the classes to the expected next class in either management and consider the frequency of each grade to be 0. In the above example, this would hateful adding the classes (4, 0) and (18, 0) – since the expected next class mark on the left-paw side is 4 and on the right-hand side is 0.
Frequency polygons from histograms
Frequency polygons share many similarities with Histograms. Both histograms and frequency polygons are used to graphically correspond frequency distribution. While frequency polygons tin can exist fatigued with or without a corresponding histogram, it is very easy to obtain a frequency polygon from a given histogram.
To draw a frequency polygon from a given histogram, join the middle of the top of each bar of the histogram sequentially.
This is effectively equivalent to the aforementioned process that we followed to draw our frequency polygon. The horizontal middle of the bar of a histogram is the class marker, and the top of the histogram is the corresponding frequency. Thus the middle of the top of each bar gives the point to plot on the graph, and by joining these points we get the frequency polygon.
Example
Frequency polygon from a histogram. Image: ECDC CC BY iv.0
In the to a higher place example, the frequency polygon is obtained by joining the middle of the summit of each bar of the histogram sequentially.
Frequency Polygons - Central takeaways
-
A frequency polygon is a graphical representation of a data set up with frequency information. It is one of the most mutual statistical tools used to represent and analyse grouped statistical data.
-
To draw a frequency polygon from a given grouped frequency distribution, we must plot the frequency against the course marks and non the class boundaries.
-
While frequency polygons can exist drawn with or without a corresponding histogram, information technology is very easy to obtain a frequency polygon from a given histogram.
Frequency Polygons
A frequency polygon is a graphical representation of a information set with frequency information. It is ane of the most usually used statistical tools used to correspond and analyse grouped statistical data.
To draw a frequency polygon, follow the post-obit steps:
1) Notice the grade mark for each class interval of the frequency distribution.
Class mark = (upper limit + lower limit)/2
ii) Plot the course marks along the horizontal axis and the frequencies along the vertical axis.
3) For each form mark, plot the frequency corresponding to that class on the graph.
4) Join all the plotted points in sequential order (connect the first point with the second, then the 2nd to the 3rd, so on…)
5) The resulting figure is the necessary frequency polygon.
A frequency polygon is one of the well-nigh commonly used statistical tools used to represent and clarify grouped statistical data. The use of a frequency polygon has been shown to be very useful for trend analysis and data recall.
Final Frequency Polygons Quiz
Source: https://www.studysmarter.de/en/explanations/math/statistics/frequency-polygons/
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