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Applications of Histograms

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Stem and Leaf Plots - Answer Key

Graphing the number of hours you and your friends spend gaming

Topic

Graphing the numbers hours you and your spend gaming

Vocabulary

  • Stem-and-Leaf Plot
  • Histogram
  • Range
  • Frequency distribution table
  • Bins

Student Exploration

How many hours do you and your friends spend gaming?

“Call of Duty: Black Ops” players have killed the equivalent of nine times the world’s population.

A recent article by msnb.com Tech reported that “Call of Duty: Black Ops” players have killed the equivalent of nine times the world’s population and played for the duration of 161 times that of World War II. See the following article for more information, http://www.ingame.msnbc.msn.com/technology/ingame/call-duty-players-have-killed-world-nine-times-125299.

And it is not just “Call of Duty: Black Ops” gamers that are busy killing, “Halo” players have killed each other 136,128,511,043 times and for 2,060,196,113 hours. According to the following report, http://www.bungie.net/stats/reach/online.aspx.

A Xbox videogame controller.

How do you and your friends measure up? How much time do you spend gaming? Survey twenty of your gamer friends and ask them the number of hours per week that they normally spend playing video games^*. Record the data from your survey and then present it in three forms.

1. Present the data from your video game survey in a stem-and-leaf plot.
2. Present the data from your video game survey in a histogram graph.
3. Create a histogram on your TI-83 calculator.

^* If you and your friends do not play video games, then do this same activity for a hobby of interest to you.

Extension Investigation

Nintendo videogame controller.

Need help graphing? Follow the steps in #4 for the stem-and-leaf plot, #5 for the histogram, and #6 for the calculator-generated histogram.

The graphs will depend on the survey results for each student. Below are examples of the graphs that students could produce. The data set used for the example is: 4, 10, 15, 20, 7, 17, 9, 2, 3, 10, 11, 25, 30, 5, 3, 12, 8, 15, 6, and 16.

4. For the stem-and-leaf plot, examine the data from your survey. Then set up the stem for your stem-and-leaf plot. Your stem need to be arranged vertically from the tens digit of your smallest value through the tens digit of your largest value (this might be a hundreds digit if your friends are serious gamers). After you set up the stem, then make the leaves! Write the leaves horizontally on the right of its stem. For more in-depth instructions revisit the “read” tab for “Stem-and-Leaf Plots.”
For the data set above here is the corresponding stem-and-leaf plot.
\begin{array}{|c|c c c c c c c c c} 0 & 2 & 3 & 3 & 4 & 5 & 7 & 8 & 9 \\1&0 & 0 & 1 & 2 & 5 & 5 & 6 & 7\\2&0 & 5\\3&0\end{array}
5. For the histogram, examine the data from your survey. Then create a frequency distribution table where you put the data in bins. A histogram should have 5 to 10 bins to make it the most meaningful. Find the range of your survey data and then divide the range by the number of bins. Then make your frequency table. Once you have made a distribution table, use it to construct the histogram. For more in-depth instructions revisit the “read” tab for “Histograms.”
The range is 27, as the minimum value is 3 and the maximum value is 30. I want to have 6 bins, so I divide 27 by 6, making each bin worth 4.5. This makes each have the following frequency.
[3-7.5) = 7, [7.5-12) = 5, [12-16.5) = 4, [16.5-21) = 2, [21-25.5) = 1, and [25.5-30) = 1.
You do not need to have six bins, you can have anywhere from 5 to 10 bins, and changing the number of bins will change the frequency of each bin and consequently the histogram.

6. For step-by-step instructions on how to create a histogram on a TI-83 calculator, revisit the “read” tab for “Applications of Histograms.”
The histogram on a calculator will correspond with the graph above.

Answer the following questions.

7.Compare your stem-and-leaf plot and histogram. How are they alike? How are they different? Explain.
For this example the stem-and-leaf plots and histogram are both strongly left skewed. You can see this as the stem for 0 and 1 contain the majority of the data for the survey and in the histogram the first bar has the highest frequency, the second bar has the second highest frequency and the third bar has the third highest frequency. They are different because the “bins” for the histogram and the stem-and-leaf plots are different. The stem-and-leaf plot has bins that coordinate with the zeros, tens, twenties, and thirds. Whereas the bins for the histogram go by 4.5, which causes the frequency to be more spread out in the histogram than the stem-and-leaf plot.
8.Describe the distribution of data in your histogram. Is it symmetrical? Right-skewed? Left-skewed? What about the data causes this type of distribution?
The distribution is left skewed as most of the people surveyed play for less than twenty hours each week and there are only three people who played for twenty hours or more.
9. What advantages do histograms have over stem-and-leaf plots? Explain.
Some of the advantages of histograms over stem-and-leaf plots are that they are very clear and strong visual of data. You can display a lot of data in a straightforward manner. The viewer can easily read a histogram and determine what is happening with the data. Similarly it is not challenging to compare the data in a histogram to a normal distribution curve.
10. What advantages do stem-and-leaf plots have over histograms? Explain.
While a stem-and-leaf plot looks like a histogram turned on its side there are several advantages to using a stem-and-leaf plot over a histogram. Stem-and-leaf plot show the data in easy to view clusters and the frequency of each interval is displayed in each leaf. In addition the individual values are also displayed within the plot, not only the frequency (as is the case with histograms).
11. For many people, viewing data visually (i.e. histogram, pie graph) is easier. In what types of situations would viewing data in a stem-and-leaf plot be better? Why?
It would be better to use a stem-and-leaf plot when you want the viewer to know the individual values in the data set.
12. What are the pros and cons of viewing and editing a calculator-generated histogram?
The calculator-generated histogram is very quick and effortless to produce, however the bins are not labeled on the graph, which makes it not as useful for in-depth analysis.
13. Scan and upload your stem-and-leaf plot and histogram to CK-12’s website to share with other students!

Resources Cited

http://www.ingame.msnbc.msn.com/technology/ingame/call-duty-players-have-killed-world-nine-times-125299

http://www.bungie.net/stats/reach/online.aspx

Connections to other CK-12 Subject Areas

  • Stem-and-Leaf Plots
  • Histograms
  • Applications of Histograms

Images from:

http://pixabay.com/en/video-user-people-character-tile-37387/

http://pixabay.com/en/joystick-box-video-controller-icon-38230/

http://pixabay.com/en/old-school-computer-video-33875/

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