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# Frequency Polygons

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Practice Frequency Polygons
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# Frequency Polygons - Answer Key

## Create a Frequency Polygon for Videogame Statistics

### Topic

Create a Frequency Polygon for Videogame Statistics

### Vocabulary

• Frequency Polygon
• Midpoint
• Interval
• Bin
• Histogram

### Student Exploration

#### How can you represent the age of gamers in a frequency polygon? Why and when is a frequency polygon a useful graph?

Many times the data from surveys is grouped according to different factors: age, usage, time, etc. This can then make it difficult to make a graphic representation for the data, however this is not the case with frequency polygons. The following tables represent the percentage of video game players (gamers) by age. The first table represents that data for new gamers, people who only played for less than two years. The second table represents data for established gamers, people who played for more than two years. The data was collected from, http://www.grabstats.com/statcategorymain.asp?StatCatID=13 and http://www.onlineeducation.net/videogame.

Table representing the percentage of new gamers (less than two years playing) by age.
Age Percentage
12-17 17
18-24 16
25-34 27
35-44 20
45-54 20
Table representing the percentage of established gamers (played for more than two years) by age.
Age Percentage
12-17 22
18-24 19
25-34 22
35-44 20
45-54 17

1. Create a frequency polygon representing the percentage of new gamers by age.

2. What does this graph tell you about the age of new gamers? Explain and give evidence.
This graph shows that the highest percentage of new gamers arearound 30-years-old. The smallest percentage of new gamers are around 21-years-old. You can tell this as the highest and lowest points on the graph are at 29.5 and 21.
3. Create a frequency polygon representing the percentage of established gamers by age

4. What does this graph tell you about the age of established gamers? Explain and give evidence.
The highest percentages of established gamers are around 14-years-old and 29.5-years-old. The lowest percentage of established gamers are around 50-years-old. You can tell this as the highest and lowest points on the graph are at 29.5 and 21.
5. Scan and upload your graph to the CK-12’s website to share with other students! You can also use educreations.com to record your discussion of your double box-and-whisker plots and then upload your video to the CK-12’s website!

### Extension Investigation

Histograms and frequency polygons are very similar graphic representations of data.

1. What are the differences of the two types of graphs? Explain.
There are several differences between the two graphs. Histograms display data in bins or categories, which are labeled on the $x-$axis, and vertical bars represent the frequency of the items in each bin, which are labeled on the $y-$axis. Frequency polygons graph the midpoints of each of the bins or categories that are displayed in histograms. Then points are plotted at each midpoint and are plotted with a horizontal height that corresponds with the frequency of that bin or category. Then the points are connected with broken lines.
2. What are the advantages of frequency polygons over histograms?
a. Give an example of a situation where they would be more useful.
One advantage of frequency polygons is that they are very easy to read and strong visuals. It is fairly easy to observe trends in the data when it is graphed as a frequency polygon. If there is a lot of data that needs to be displayed, a frequency polygon would be easier to read than a histogram. An example of a situation when a frequency polygon would be more useful is for a data set with a large population over a long period of time, such as annual median household incomes in a city over the forty years.
3. What are the advantages of histograms over frequency polygons?
a. Give an example of a situation where they would be more useful.
Histograms are also easy to read and strong visuals. The categories are labeledon the $x-$axis and it is easy to determine the frequency of the items in each category. The categories are not labeled in a frequency polygon. It is easy to compare a histogram to a normal distribution curve, more so than with frequency polygons. One disadvantage of frequency polygons is that the “anchors” on each end of the graph might make the viewer think that those are data points that are zero, this does not occur with histograms.

### Connections to other CK-12 Subject Areas

• Mean
• Ungrouped Data to Find the Mean
• Grouped Data to Find the Mean
• Histograms
• Applications of Histograms