Probability Histograms on the TI-83/84

Summary:  You can use your TI-83/84 to make a histogram for a discrete probability distribution. The process is very similar to plotting a frequency histogram, except that you set up the Window screen a little differently.

See also:  TI-83/84 Troubleshooting
Histogram of a Binomial PD on the TI-83/84

The probability distribution at right considers three trials where there is a 1/3 probability of winning any one game. It shows the probability of winning 0, 1, 2, or 3 games out of the 3. We sketched the histogram in class; now let’s use the TI-83/84 to plot it.

This particular distribution happens to be a binomial distribution, but we’re not actually using its binomial properties. You can use the TI-83/84 to plot a histogram for any discrete probability distribution.

There are three main screens: Stats Edit where you enter the numbers, Stat Plot where you set up the histogram, and Window where you set up the bar width and data ranges.

By the way, this note will use L1 and L2, but you can use any lists you like, as long as you enter the actual list numbers in the right places on the Stat Plot screen. (It doesn’t matter whether there are numbers in any other list.)

Step 1: Enter the x’s in L1 and the P’s in L2

Enter the data points.	[STAT] [1] selects the list-edit screen.   Cursor onto the label L1 at top of first column, then [CLEAR] [ENTER] erases the list. Enter the x values.
Remember that you can enter probabilities as fractions, and the TI-83/84 will convert them to decimal for you.	Cursor onto the label L2 at top of first column, then [CLEAR] [ENTER] erases the list. Enter the P(x) values.

Caution: L2 is not finished in the picture above. You need to enter the remaining probabilities in rows 3 and 4 of L2.

Step 2: Program a histogram on the Stat Plot screen

Turn off other plots.	Press [Y=]. Cursor to each highlighted = sign or Plot number and press [ENTER] to deactivate.
Turn on Stat Plot 1 as a histogram.	Press [2nd Y= makes STAT PLOT] [1] [ENTER] to turn on plot 1.
Select the histogram icon.	[▼] [►] [►] [ENTER]
Answer Xlist: with L1 because the x’s are in L1.	Press [2nd 1 makes L1] [ENTER].
Answer Freq: with L2 because the probabilities are in L2.	Press [2nd 2 makes L2] [ENTER].
To prevent the y axis messing up the picture later, turn axes off.	Press [2nd ZOOM makes FORMAT] [▼ 3 times] [►] [ENTER].

Step 3: Specify bar width and data ranges on the Window screen

The bar width should be the distance between adjacent x values, which is usually 1. To center the bars on the appropriate x values, set Xmin to the smallest x minus half a bar width and set Xmax to the largest x plus half a bar width. (You could use a different x range, which would make the histogram look right but would not center the bars on the x values.)

For instance, the number of wins in the table ranges from 0 to 3 in steps of 1; therefore the bar width is 1, half a bar width is 0.5, and the x range is −0.5 to 3.5. Think of it as a half-bar “margin” on either side of the actual data range.

Xmin must be half a bar width below the smallest x: 0−0.5 = −0.5. Xmax must be half a bar width above the largest x: 3+0.5 = 3.5.	Press [WINDOW]. [(-)] .5 [ENTER] sets Xmin. 3.5 [ENTER] sets Xmax.
Xscl is the bar width, the distance between x values.	1 [ENTER] sets Xscl
Ymin should be 0 since no probability can be less than 0.	0 [ENTER] sets Ymin
Ymax should be the at least the largest P(x). Our P’s range from 0 to 12/27; let’s use 15/27.	15 [÷] 27 [ENTER] sets Ymax
Yscl is discretionary: set it however far apart you want the dots, vertically. This should be some reasonable division of Ymax; in this case 5/27 seems like a good choice.	5 [÷] 27 [ENTER] sets Yscl.
Always set Xres to 1.	1 [ENTER] sets Xres.

Step 4: Display the graph

Press [GRAPH].

You can trace the histogram by pressing [TRACE]. This shows you “class limits”: the x value is in the middle. The height of the bar, labeled “n”, is the probability. Press [◄] and [►] to show the information for other classes. To suppress the tracing information, press [GRAPH] again.

In the example at right, the “class limits” are .5 and 1.5; therefore this is the x=1 bar of the histogram. The probability is 0.4444, which is 12/27.