Frequency Histograms and Polygons the Easy Way on the TI-83/84

Getting the program

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

• If a classmate has the program on her calculator (any model TI-83/84), she can transfer it to yours with 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].
• Or, download HISTNPG2.ZIP (21 KB, updated Sep 21, 2008), unzip it, and transfer file HISTNPG2.8XP to your calculator. (This requires TI-Connect or TI-Graph Link software software and a cable.)
• Or, as a last resort, key in the program. See HISTNPG2.PDF and HISTNPG2_HINTS.HTM in the HISTNPG2.ZIP file.

Using the program

To use the program, put the class marks or data in a statistics list and the frequencies (if applicable) in another.

Then press [PROG], select HISTNPG2, and press [ENTER] [ENTER]. The program will prompt you for the necessary information and will check silently to make sure your inputs are in valid form. Then it will ask whether you want a histogram, polygon, or both, and will produce your desired graph. (The program uses an algorithm to ensure that there are an appropriate number of dots vertically on the screen.)

If you should ever need to break out of the program before finishing the prompts, press [ON] [1].

Technical details

If you have frequency data, the data list and frequency list must be the same length and the class widths in the data list must all be the same; the program checks this. The TI-83 and TI-84 won’t let you make a histogram with more than 47 classes, and the program also checks this. Finally, the program also won’t let you make a grouped frequency histogram with just one or two classes, because that’s silly.

The program uses some variables for temporary storage and leaves them afterward in case you want to look at them:

A = upper bound of highest class

I = scratch variable for use in lists

N = number of classes

W = class width

LD = class marks

LF = class frequencies

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

If you want to delete the single-letter variables, though it’s hardly worth the effort, press [2nd + makes MEM] [2] [2], cursor to each one, and press [DEL].

Example 1: Grouped Frequency Data

The grouped frequency distribution at right shows the ages reported by Roman Catholic nuns, from Johnson & Kuby, Elementary Statistics 9/e (Thomson, 2004), page 67. Show the data as a histogram and as a frequency polygon.

Solution: Your class marks are 25, 35, up through 85, and your class width is 10. On the STAT EDIT screen, enter those marks in one list and the frequencies in another. Here the class marks have been entered in L5 and the frequencies in L6, just for variety.

Run the HISTNPG2 and specify frequency distribution. The program then asks you to identify the lists, and which plots you want. In the illustration, I’m selecting both plots. If you’re not doing frequency polygons in your class, select [1] for just the histogram.

The output is shown at right, once with the histogram and polygon on the same screen, and once with just the histogram. It’s quite similar to the graphs done “by hand”, except that the vertical spacing of the dots may be different.

optional extra: Tracing the histogram or polygon

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

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

To trace the polygon, if you selected both, press [TRACE] [▼]. This lets you see the class marks and number of data points in each class, instead of the class boundaries.

Why press [▼]? When you press [TRACE], the calculator starts with a trace of Stat Plot 1. The up or down cursor key moves 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.

Example 2: List of Numbers

Suppose you want to make a histogram of the class performance on a 15-point quiz, where the scores are shown at left. You don't want to bother to group these 23 scores by hand, so you enter them in a statistics list such as L1 and let the program do the grouping for you.

Run the HISTNPG2 program and select [2] for a plain list of numbers. The program asks you for the list that contains the data. It also needs to know how you want to group the numbers, so it asks for the lower bound of the first class and for the class width. Since 0 is the lowest possible grade, that’s the obvious lower bound for this example. The quiz has a possible maximum score of 15, and 10% of that is 1.5 points. This is a good class width because D, C, B, and A will each be one bar of the histogram.

At this point you may see a pause as the program computes the number of classes and places each data point into a class. (It uses statistics lists LD for the class marks and LF for the computed frequencies.)

Finally, the program asks whether you want a histogram, frequency polygon, or both. I’ve selected a histogram, and you see the result.

optional extra: Tracing the histogram

At first glance you might think there are four Ds, three Cs, two Bs, and one A. But when you check this by pressing [TRACE] you see that’s not correct. The highest class is the 15 to 16.5 class, since someone had a perfect score of 15. (Remember that when a value is right on a class boundary, it is always assigned to the higher class.) So the top two classes in the histogram represent As (three students), the next lower is the three Bs, the next lower (shown at right) is four Cs, the next lower is two Ds, and the rest are Fs.

Example 3: Ungrouped Frequency Distribution

You have recorded the numbers of children in 30 randomly selected families that used a community center in a given week, and you want to show a picture of the distribution. There are only a few diffeent values (numbers of children per family), so you chose an ungrouped frequency distribution.

Enter the data in two lists such as L3 and L4, and run the HISTNPG2 program. Select [1] since you have a frequency distribution, even though it is ungrouped.

When prompted, enter the data list and frequency lisyt, and select whether you want a histogram, a frequency polygon, or both. I’ve selected a histogram, and the results are shown in the third screen shot below.

The vertical line in the histogram is the y axis — you can remove it, if you want, by pressing [2nd ZOOM makes FORMAT] and selecting AXES OFF. Also in the histogram, notice that the vertical rows of dots run through the center of each bar rather than along the edges. This reminds you that you should label the bars of an ungrouped frequency distribution under the centers, not the edges as you label a grouped histogram.

If you want to trace the ungrouped frequency histogram, follow the same procedure as for tracing a grouped frequency histogram.

What’s New

Sep 21, 2008:

• rewrote the program to handle plain lists as well as frequency distributions and changed its name from HISTNPGN to HISTNPG2; also added more error checking to the program and ensured Ymin is always ≥1
• added Example 2 and Example 3 so that all three types of problems are illustrated
• added a description of the restrictions on the data and instructions to break out if necessary
• added a screen shot of just the histogram in Example 1
• added a table of contents

Jun 7, 2008:

• new document extracted from Frequency Polygons on the TI-83/84, which was not an intuitive place to find a program for histograms
• revised the program to check equal class widths and equal list lengths and to use two lists instead of four