Histogram of a Binomial PD on the TI-83/84

Summary:  You can use your TI-83/84 to make a histogram for a binomial probability distribution, as a special case of the discrete probability histogram.

See also:  TI-83/84 Troubleshooting

Let’s illustrate with a histogram of the binomial distribution for n = 15, p = 0.4.

There are three main screens: the home screen where you fill the lists, 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

Unlike the general discrete distribution, for a binomial distribution we can use functions to fill up the two lists that will be plotted in the histogram:

• The seq function creates the list of x’s (possible numbers of successes) for us. The general form is seq(X,X,0,n). (It’s actually considerably more general than that, but this form will get what we need.)
• The binompdf function computes the probabilities, as explained in Binomial Probability Distribution on the TI-83/84. The general form is binompdf(n,p).

To get the function seq(X,X,0,15), start by selecting the seq function.	[2nd STAT makes LIST] [►] [5]
Enter the arguments and closing parenthesis, and store the result in list L1.	[x,T,θ,n] [,] [x,T,θ,n] [,]   [0] [,] [1] [5] [)]   [STO→] [2nd 1 makes L1] [ENTER]
Now select the binompdf function. The arguments are n and p, and you store the result in list L2.	To select binompdf on the TI-83, press [2nd VARS makes DISTR] [0]. On the TI-84, press [2nd VARS makes DISTR] [ALPHA MATH makes A].   15 [,] .4 [,] [)] [STO→] [2nd 2 makes L2] [ENTER]
Optional: Later, you’ll need to set up a top margin on the Window screen. You can either guess, plot the histogram, and adjust the window parameters, or you can find out the highest probability now by using max(L2).   The highest probability is just under 0.21, so we’ll use that value in Step 3 on the Window screen.	To find the highest probability in the distribution, press [2nd STAT makes LIST] [◄] [2] [2nd 2 makes L2] [)] [ENTER].

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].

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

The left and right edges of the screen are 0 to n+1.	Press [WINDOW]. [0] [ENTER] sets Xmin. 16 [ENTER] sets Xmax.
Xscl is the bar width, the distance between x values, which is always 1.	[1] [ENTER] sets Xscl
Ymin is 0 since no probability can be less than 0.	[0] [ENTER] sets Ymin
Ymax should be the at least the largest P(x). If you found the value in Step 1 by using max(L2), type it in here. Otherwise, make a guess and you can adjust it later, after seeing the histogram.	.21 [ENTER] sets Ymax to the value that was found in Step 1.
Yscl is discretionary: set it however far apart you want the dots vertically. 0.1 is probably a good choice.	[.] [1] [ENTER] sets Yscl.
Always set Xres to 1.	[1] [ENTER] sets Xres.

Step 4: Display the graph

Press [GRAPH].   Here is the histogram for binompdf(15,0.4).

You can trace the histogram by pressing [TRACE]. The value labeled min= is x, the number of successes. The height of the bar, labeled n, is the probability. Press [◄] and [►] to show the information for other x values.

In the example at right, the min is 3 and n is 0.063387...; therefore P(3) = 0.0634.

To suppress the tracing information, press [GRAPH] again.