Chapter 2: Descriptive Statistics

2.8 Using Technology for Charts and Graphs

Learning Objectives

By the end of this section, the student should be able to:

  • use technology to draw charts and graphs

This is another section to show technology tools that can be used to help with the statistics concepts taught in this chapter. This section will cover tools to help create visual representations of data: charts and graphs.

Graphing Calculator

Similar to all the other technology sections, the main tool introduced will be the TI-83, 83+, 84, or 84+ Graphing Calculator. Using the graphing calculator for creating charts and graphs is possible, though some of the additional technology tools might give you a better visual of your graph. Let's start with a common chart in statistics - a histogram.

 

Histograms

A graph that can be done in the graphing calculator is a histogram, which is covered in 2.2 Histograms, Frequency Polygons, and Time Series Graphs. Before looking at a specific example, here are general instructions for setting up the graphing calculator to draw a histogram. The instructions show how to construct two histograms with the built-in STAT PLOT application. The first way will use the default ZOOM. The second way will involve customizing a new graph. These instructions are to do be followed after the data is already entered in the graphing calculator.

Drawing Histograms using the TI-83, 83+, 84, or 84+ Graphing Calculator

  1. Access graphing mode by pressing 2nd key, [STAT PLOT].

  2. Select <1:Plot1> to access plotting of the first graph. Highlight over <1:Plot1> and press enter key.

  3. Use the arrows navigate go to <ON> to turn on Plot 1. Highlight over <ON> and press enter key.

  4. On <Type>, use the arrows to highlight the histogram picture (the 3rd picture) and select it by pressing enter key.
  5. Use the arrows to navigate to <Xlist>. If <L1> is not showing, select it by pressing 2nd key, [L1], enter key.
  6. Use the arrows to navigate to <Freq>. Assign the frequencies to <L2> by pressing 2nd key, [L2], enter key.

  7. Go back to the graphing move by pressing 2nd key, [STAT PLOT].

  8. Use the arrows to turn off the remaining plots by following steps 2 - 3. After selecting <2:Plot2> and <3:Plot3> use the arrows navigate go to <OFF> to turn off each Plot. Highlight over <OFF> and press enter key.
  9. Note: Selecting <4:PlotsOff> and pressing enter key will turn off all Plots at the same time.

The STAT PLOT feature does not work when there are equations in the graphing calculator. Be sure to deselect or clear all equations before graphing.

To deselect equations:

  1. Access the list of equations by pressing Y= key.

  2. Select each equal sign <=> by using the arrow down key and arrow right key keys and pressing enter key to unhighlight/deselect them.

  3. Continue, until all equations are deselected.

To clear equations:

  1. Access the list of equations by pressing Y= key.

  2. Use the arrow keys, arrow down key and arrow right key, to navigate to the right of each equal sign <=> and clear them by pressing clear key.

  3. Repeat until all equations are deleted.

Once the equations are deselected or cleared, the two options to draw default histogram are:

To use the default ZOOM:

  1. Access the ZOOM menu by pressing ZOOM key.

  2. Use the arrow down key key to select <9:ZoomStat> or press the number 9 key key.

  3. The histogram will show with a window automatically set.

To draw custom histogram:

  1. Access window mode by pressing window key to set the graph parameters.
  2. Set the following window parameters:
    • \({X}_{\mathrm{min}}=\) (starting point value)
    • \({X}_{\mathrm{max}}=\) (ending point value)
    • \({X}_{scl}=1\) (width of bars)
    • \({Y}_{\mathrm{min}}=0\)
    • \({Y}_{\mathrm{max}}=\) (above the highest frequency value)
    • \({Y}_{scl}=1\) (spacing of tick marks on y-axis; adjusted to scale as needed)
    • \({X}_{res}=1\)
  3. Access graphing mode by pressing graph key to see the histogram.

Legend

  • A blank calculator button represents a button press
  • [ ] represents yellow command or green letter behind a key
  • < > represents items on the screen

Now that the instructions of how to draw a histogram were provided, let's revisit this example from 2.2 Histograms, Frequency Polygons, and Time Series Graphs:

Example

The following data are the number of books bought by 50 part-time college students at ABC College. The number of books is discrete data, since books are counted.

1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1

2; 2; 2; 2; 2; 2; 2; 2; 2; 2

3; 3; 3; 3; 3; 3; 3; 3; 3; 3; 3; 3; 3; 3; 3; 3

4; 4; 4; 4; 4; 4

5; 5; 5; 5; 5

6; 6

Eleven students buy one book. Ten students buy two books. Sixteen students buy three books. Six students buy four books. Five students buy five books. Two students buy six books.

Instead of doing a histogram by hand, here are calculator instructions for entering the data from this example into the graphing calculator and then creating a customized histogram:

Press stat key, highlight over <1:Edit> and press enter key.

If <L1> has data in it, arrow up into the name <L1>, press clear key and enter key. Then arrow into the name <L2>, and if necessary, do the same for <L2>.

Into <L1>, enter the data values: 1, 2, 3, 4, 5, 6. Type each number, then press enter key.

Into <L2>, enter frequency of each value: 11, 10, 16, 6, 5, 2. Type each number, then press enter key.

After entering in the data, remember to follow the instructions for drawing the histogram (setting the [STAT PLOT]) and deselecting/clearing any equations, as stated above on this page.

For this example, we will create a customized histogram and set our window accordingly:

  • Press window key and set the following:
    • \({X}_{\mathrm{min}}=0.5\)
    • \({X}_{\mathrm{max}}=6.5\)
    • \({X}_{scl}=1\) (width of bars; for this example is (6.5 – .5)/6)
    • \({Y}_{\mathrm{min}}=–1\)
    • \({Y}_{\mathrm{max}}=20\) (above the highest frequency value)
    • \({Y}_{scl}=1\) (spacing of tick marks on y-axis)
    • \({X}_{res}=1\)

Access graphing mode by pressing graph key to see the histogram. Using the trace key key and the arrow keys can help to examine the histogram. The histogram displayed on the calculator should look like the figure shown in the example on section 2.2 Histograms, Frequency Polygons, and Time Series Graphs.

Legend

  • A blank calculator button represents a button press
  • [ ] represents yellow command or green letter behind a key
  • < > represents items on the screen

 

Box Plots

Another graph that can be drawn using the graphing calculator is the box plot or box-and-whisker plot that was covered in 2.4 Box Plots. Before looking at a specific example, below are general instructions for setting up the graphing calculator to draw a box plot - which is similar to how we set up the calculator to draw a histogram. The instructions show how to construct two types of box plots with the built-in STAT PLOT application: one without outliers and one with outliers. with the built-in STATPLOT application. Also, the box plot can be done without a frequency list. Either way, these instructions are to do be followed after the data is already entered in the graphing calculator.

Drawing Box Plots using the TI-83, 83+, 84, or 84+ Graphing Calculator

  1. Access graphing mode by pressing 2nd key, [STAT PLOT].

  2. Select <1:Plot1> to access plotting of the first graph. Highlight over <1:Plot1> and press enter key.

  3. Use the arrows navigate go to <ON> to turn on Plot 1. Highlight over <ON> and press enter key.

  4. On <Type>, use the arrows to highlight the box plot of choice and select it by pressing enter key:
    • Box plot picture (the 4th picture) is with outliers.
    • Box plot picture (the 5th picture) is without outliers
  5. Use the arrows to navigate to <Xlist>. If <L1> is not showing, select it by pressing 2nd key, [L1], enter key.
  6. Use the arrows to navigate to <Freq>.
    • If all the data is being put into <L1>, then assign the frequencies to <1> by pressing alpha key, number 1 key, enter key.
    • If data is being put into <L2>, assign the frequencies to <L2> by pressing 2nd key, [L2], enter key.
  7. If the choice was the box plot with outliers, use the arrows to navigate to <Mark> and select the image that will appear for a data value that is an outlier.
  8. Go back to the graphing move by pressing 2nd key, [STAT PLOT].
  9. Use the arrows to turn off the remaining plots by following steps 2 - 3. After selecting <2:Plot2> and <3:Plot3> use the arrows navigate go to <OFF> to turn off each Plot. Highlight over <OFF> and press enter key.
  10. Note: Selecting <4:PlotsOff> and pressing enter key will turn off all Plots at the same time.

Reminder: The STAT PLOT feature does not work when there are equations in the graphing calculator. Be sure to deselect or clear all equations before graphing. Follow the directions stated above under "Drawing Histograms using the TI-83, 83+, 84, or 84+ Graphing Calculator."

Once the equations are deselected or cleared, the box plot can be viewed by pressing graph key or accessing the ZOOM menu by pressing ZOOM key and then using the arrow down key key to select <9:ZoomStat> or pressing the number 9 key key. The box plot will show with a window automatically set.

Legend

  • A blank calculator button represents a button press
  • [ ] represents yellow command or green letter behind a key
  • < > represents items on the screen

Now that the instructions of how to draw a box plot were provided, let's revisit this example from 2.4 Box Plots:

Example

The following data are the heights of 40 students in a statistics class.

59; 60; 61; 62; 62; 63; 63; 64; 64; 64; 65; 65; 65; 65; 65; 65; 65; 65; 65; 66; 66; 67; 67; 68; 68; 69; 70; 70; 70; 70; 70; 71; 71; 72; 72; 73; 74; 74; 75; 77

Construct a box plot.

    Let's assume we were not given the value of the minimum, maximum, [latex]Q_1[/latex], [latex]Q_2[/latex], and [latex]Q_3[/latex] as was in the example. To construct the box plot using the graphing calculator for this example, there are three options:

    1. Enter in all the data into a single list and have the calculator draw the box plot
    2. Enter the data values in one list, the frequencies in another list, and have the calculator draw the box plot
    3. Have the calculator find the minimum, maximum, [latex]Q_1[/latex], [latex]Q_2[/latex], and [latex]Q_3[/latex] and then draw the box plot by hand. We won't do this option here, because section 2.9 Using Technology for Descriptive Statistics will show how to calculate these values.

    Let's do option 1 and option 2. The option you choose is a matter of preference, but one tip - option 2 is easier if there are a lot of repeated data values.

    Option 1.

    Press stat key, highlight over <1:Edit> and press enter key.

    If <L1> has data in it, arrow up into the name <L1>, press clear key and enter key. Then arrow into the name <L2>, and if necessary, do the same for <L2>.

    Into <L1>, enter the data values: 59; 60; 61; 62; 62; 63; 63; 64; 64; 64; 65; 65; 65; 65; 65; 65; 65; 65; 65; 66; 66; 67; 67; 68; 68; 69; 70; 70; 70; 70; 70; 71; 71; 72; 72; 73; 74; 74; 75; 77. Type each number, then press enter key.

    After entering in the data, remember to follow the instructions for drawing the box plot (setting the [STAT PLOT]) and deselecting/clearing any equations, as stated above on this page.

    Option 2.

    Press stat key, highlight over <1:Edit> and press enter key.

    If <L1> has data in it, arrow up into the name <L1>, press clear key and enter key. Then arrow into the name <L2>, and if necessary, do the same for <L2>.

    Into <L1>, enter the data values: 59; 60; 61; 62; 63;64; 65; 66; 67; 68; 69; 70; 71; 72; 73; 74; 75; 77. Type each number, then press enter key.

    Into <L2>, enter frequency of each value: 1; 1; 1; 2; 2; 3; 9; 2; 2; 2; 1; 5; 2; 2; 1; 2; 1; 1. Type each number, then press enter key.

    After entering in the data, remember to follow the instructions for drawing the box plot (setting the [STAT PLOT]) and deselecting/clearing any equations, as stated above on this page.

    Access graphing mode by pressing graph key or accessing the ZOOM menu by pressing ZOOM key and then using the arrow down key key to select <9:ZoomStat> or pressing the number 9 key key. Using the trace key key and the arrow keys can help to examine the box plot. The box plot in the example from 2.4 Box Plots is without outliers, so be sure you select the appropriate picture in the [STAT PLOT] if you want to check that it looks like the figure shown in the example.

     

    Helpful Videos for the Graphing Calculator

    Below are links to helpful videos for using the graphing calculator for the concepts covered on this page:

     

    Additional Technology Tools

    In addition to the graphing calculator, there are some additional technology tools that can be used for the concepts covered on this page. Below are links to helpful videos for those tools:

     

    Section Practice

    The table below contains the 2010 obesity rates in U.S. states and Washington, DC.

    Table 1: Obesity Rates in % for each US State and Washington DC
    State Percent (%) State Percent (%) State Percent (%)
    Alabama 32.2 Kentucky 31.3 North Dakota 27.2
    Alaska 24.5 Louisiana 31.0 Ohio 29.2
    Arizona 24.3 Maine 26.8 Oklahoma 30.4
    Arkansas 30.1 Maryland 27.1 Oregon 26.8
    California 24.0 Massachusetts 23.0 Pennsylvania 28.6
    Colorado 21.0 Michigan 30.9 Rhode Island 25.5
    Connecticut 22.5 Minnesota 24.8 South Carolina 31.5
    Delaware 28.0 Mississippi 34.0 South Dakota 27.3
    Washington, DC 22.2 Missouri 30.5 Tennessee 30.8
    Florida 26.6 Montana 23.0 Texas 31.0
    Georgia 29.6 Nebraska 26.9 Utah 22.5
    Hawaii 22.7 Nevada 22.4 Vermont 23.2
    Idaho 26.5 New Hampshire 25.0 Virginia 26.0
    Illinois 28.2 New Jersey 23.8 Washington 25.5
    Indiana 29.6 New Mexico 25.1 West Virginia 32.5
    Iowa 28.4 New York 23.9 Wisconsin 26.3
    Kansas 29.4 North Carolina 27.8 Wyoming 25.1
    1. Use a random number generator (as discussed in Section 1.5 Using Technology page) to randomly pick eight states. Construct a bar graph of the obesity rates of those eight states.
    2. Construct a bar graph for all the states beginning with the letter "A."
    3. Construct a bar graph for all the states beginning with the letter "M."
    Solution

    For question 1, an example solution for using the random number generator for the TI-84+ to generate a simple random sample of 8 states. Instructions are as follows.

    • Number the entries in the table 1–51 (Includes Washington, DC; Numbered vertically)
    • Press MATH
    • Arrow over to PRB
    • Press 5:randInt(
    • Enter 51,1,8)

    Eight numbers are generated (use the right arrow key to scroll through the numbers). The numbers correspond to the numbered states (for this example: {47 21 9 23 51 13 25 4}. If any numbers are repeated, generate a different number by using 5:randInt(51,1)). Here, the states (and Washington DC) are {Arkansas, Washington DC, Idaho, Maryland, Michigan, Mississippi, Virginia, Wyoming}.

    Corresponding percentages are {30.1, 22.2, 26.5, 27.1, 30.9, 34.0, 26.0, 25.1}.

    A bar graph showing 8 states on the x-axis and corresponding obesity rates on the y-axis.
    Figure 1. Bar Chart of US States and Obesity Rate %
    The bar graph for question 2:
    A bar graph showing 8 states on the x-axis and corresponding obesity rates on the y-axis.
    Figure 2. Bar Chart of US States Beginning with Letter "A"

     

    The bar graph for question 3:

    This is a bar graph that matches the supplied data. The x-axis shows states, and the y-axis shows percentages.
    Figure 3. Bar Chart of US States Beginning with Letter "M"

    Suppose that three book publishers were interested in the number of fiction paperbacks adult consumers purchase per month. Each publisher conducted a survey. In the survey, adult consumers were asked the number of fiction paperbacks they had purchased the previous month. The results are as follows:

    Table 2: Publisher A Survey Results
    # of books Freq. Rel. Freq.
    0 10
    1 12
    2 16
    3 12
    4 8
    5 6
    6 2
    8 2
    Table 3: Publisher B Survey Results
    # of books Freq. Rel. Freq.
    0 18
    1 24
    2 24
    3 22
    4 15
    5 10
    7 5
    9 1
    Table 4: Publisher C Survey Results
    # of books Freq. Rel. Freq.
    0–1 20
    2–3 35
    4–5 12
    6–7 2
    8–9 1
    1. Find the relative frequencies for each survey. Write them in the charts.
    2. Using either a graphing calculator or computer, use the frequency column to construct a histogram for each publisher's survey. For Publishers A and B, make bar widths of one. For Publisher C, make bar widths of two.
    3. In complete sentences, give two reasons why the graphs for Publishers A and B are not identical.
    4. Would you have expected the graph for Publisher C to look like the other two graphs? Why or why not?
    5. Make new histograms for Publisher A and Publisher B. This time, make bar widths of two.
    6. Now, compare the graph for Publisher C to the new graphs for Publishers A and B. Are the graphs more similar or more different? Explain your answer.

     

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