Frequency Polygons on the TI-83/84

See also:  TI-83/84 Troubleshooting
Histograms of Numeric Data on the TI-83/84
Descriptive Statistics of a Data Set on the TI-83/84

Step 1: Deactivate all other graphs

Deactivate any graphs that are already set up, so that they don’t interfere with your new graph.

(As an alternative to PlotOff and FnOff, you might prefer to press [Y=] and de-highlight Plot1 through Plot3 as well as Y1 through Y0. That’s fine, as long as you remember to scroll down to check Y8, Y9, and Y0, and look up to check the three plots at the top of the Y= screen. Many people forget, but with PlotOff and FnOff you can’t forget.)

Steps 2–4 set up three screens. You can do them in any order — the order shown here isn’t critical.

Step 2: Add two classes with zero frequencies

Compared to the histogram, the frequency polygon needs one extra class mark at the left (low end) and one at the right (high end), both with zero frequencies. This puts both ends of the polygon on the x axis.

Assuming you’ve already entered your class marks in L1 and your frequencies in L2, you need to insert one row before the first row and add one row after the last.

Step 3: Specify bar width and margins on the Window screen

The settings are quite similar to a grouped frequency histogram. In fact, only Xmin and Xmax are different, but for simplicity all seven variables will be shown here.

Press [WINDOW] to get to the Window screen, and then enter values as follows:

• Xmin is one class width below the lower boundary of the first class.
• Xmax is one class width above the upper boundary of the last class.

If the class boundaries are 150 to 250, 250 to 350, and so on up to 950 to 1050, then your class width is 100. Xmin is 150−100 = 50, and Xmax is 1050+100 = 1150.

• XScl is the class width.
• Ymin is always 0 since frequencies can’t be negative.
• Ymax is ≥ the largest of the frequencies.
• Yscl is some convenient division of Ymax. For instance, if Ymax is 915 you might set Yscl to 100
• Xres is always 1.

Step 4: Program the frequency polygon on the Stat Plot screen

Turn on Stat Plot 2 as an x-y line graph.	Press [2nd Y= makes STAT PLOT] [2] [ENTER] to turn on plot 2. Caution: make sure you press [ENTER] to turn the plot on. Many people press the down arrow instead, so that the plot is still turned off.
Select the x-y line icon.	[▼] [►] [ENTER]
Answer Xlist: with L1 because the class marks are in L1.	Press [▼] [2nd 1 makes L1].
Answer Freq: with L2 because the frequencies are in L2.	Press [2nd 2 makes L2] [ENTER].
Select a marker for the corners of the polygon.	Select □ or + for visibility.

Step 5: Display the graph

Press [GRAPH] to display the graph.

You can display the frequency polygon as an overlay on the histogram. (The calculator can display up to three stat plots at the same time.) Just set up Stat Plot 1 for a histogram with the same two lists. No bars will appear for the two class marks with zero frequencies.

Example

The grouped frequency distribution at right is the ages reported by Roman Catholic nuns, from Johnson & Kuby, Elementary Statistics 9/e (Thomson, 2004), page 67. Use your TI-83/84 to plot a frequency polygon.

To begin, clear old plots. Then, enter the class marks in L1 and the frequencies in L2.

Your class marks are 25, 35, up through 85, and your class width is 10. Therefore you need extra class marks 15 and 95. Insert the class mark of 15 at the beginning of L1, and insert a zero frequency at the beginning of L2.

Move to the end of L1 and add your class mark of 95, then add a zero frequency at the end of L2. If you’ve done it right, each list will have nine numbers.

Next, press [WINDOW] and fill in the values according to the rules given above:

• Xmin = one class width below lower boundary of first class = 20−10 = 10.
• Xmax = one class width above upper boundary of last class = 90+10 = 100.
• Xscl = class width = 10.
• Ymin = 0.
• Ymax ≥ the highest frequency = 254.
• Yscl = a convenient division of Ymax — use 50.
• Xres = 1.

Finally, set up the Stat Plot screen and press [GRAPH]. The result is shown below right.

You can overlay the frequency polygon on the grouped frequency histogram. Simply set up Stat Plot 1 with the histogram, while leaving Stat Plot 2 turned on. The result is shown below left.

optional extra: Trace the polygon

You can trace the polygon by pressing [TRACE] [▼]. This lets you see the class marks and number of data points in each class.

Why press [▼]? When you press [TRACE], the calculator starts with a trace of Stat Plot 1. The up or down cursor key will move between plots. Since the frequency polygon is Stat Plot 2, you are tracing it when you see P2 in the upper left corner, as shown in the illustration.

Press [◄] and [►] to move through the classes. To suppress the tracing information, press [GRAPH] again.

TI-83/84 program HISTNPGN

I’ve developed a TI-83/84 program that graphs a frequency polygon or histogram, or both.

Getting the program

There are three methods to get the program into your calculator:

• If you have the TI-Connect or TI-Graph Link software and a cable, download HISTNPGN.ZIP (4 KB), unzip it, and transfer file HISTNPGN.8xp to your calculator. (If nothing happens when you double-click the HISTNPGN.ZIP file, you need a ZIP program; I recommend WinZip.)
• If a classmate already has the program on her calculator, you can transfer it to yours by using the short cable with headphone-style plugs that comes with all TI calculators. On your calculator, press [2nd x,T,θ,n makes LINK] [►] [ENTER], and then on hers press [2nd x,T,θ,n makes LINK] [3], select the program, then press [►] [ENTER]. (It’s okay if you don’t have the same exact model, as long as each one is a TI-83 or TI-84.)
• If you don’t have the software and cable, and you can’t get the program from a classmate, you can key it in. For the complete source code of the program, download the HISTNPGN.ZIP file as above, and then double-click on HISTNPGN_SourceCode.htm within the ZIP file.

Using the program

To use the program, put the class marks in one list and the frequencies in another. (Enter only the real classes, not the extra classes below and above the real classes. The program will create the extra classes for you.) Then press [PROG], select HISTNPGN, and press [ENTER] [ENTER]. The program will prompt you for the lists containing the class marks and the frequencies. Here the class marks have been entered in L5 and the frequencies in L6, just for variety.

After you identify the lists, the program asks you which plots you want. I’m selecting both plots.

The output is quite similar to the graphs done “by hand” above, except that the vertical spacing of the dots is different. The program uses an algorithm to ensure that there are between 10 and 20 vertical divisions for most data sets.

Technical details: The program uses variables N, W, and X for temporary storage. It stores the class marks and frequencies for the histogram in lists LD and LF, and the class marks and frequencies for the polygon in lists LPD and LPF.

If you want to delete the variables, press [2nd + makes MEM] [2] [2], cursor to each one, and press [DEL]. (X is a system variable and can’t be deleted.)

If you want to delete the lists, press [2nd + makes MEM] [2] [4], scroll down to find each one, and press [DEL].