# Calculator Programs and the AP Statistics Exam

## Calculator Programs

Often questions arise about programs that can be added to calculators to improve their functionality or ease of use. Sometimes these programs are purchased software packages, while other times they are the creation of a teacher or student with programming skills. The conscientious teacher often asks, "Is a program like this allowed on the AP Exam?" This article seeks to clarify these questions.

The College Board policy on calculator usage states:

*For the exam, you're not allowed to access any information in your graphing calculators or elsewhere if it's not directly related to upgrading the statistical functionality of older graphing calculators to make them comparable to statistical features found on newer models. The only acceptable upgrades are those that improve the computational functionalities and/or graphical functionalities for data you key into the calculator while taking the examination. Unacceptable enhancements include, but aren't limited to, keying or scanning text or response templates into the calculator.*

Source of this quotation: AP^{®}: Calculator Policy

This policy is the key to determining which type of programs are allowed. A number of commonly used programs clearly fit in this category. The TI-83 Plus and TI-84 Plus now come preloaded with a flash-app program entitled *Catalog Help*. This program guides the user with prompts for the various variables you enter. For example, the **normalcdf** command requires you enter first the **lowerbound**, then the **upperbound**, then, optionally, µ and Ã. The *Catalog Help* program simply reminds you of the order that these variables are entered. Not requiring students to remember the order of these variables is one of the most frequently requested improvements that teachers have for the ubiquitous 83 Plus/84 Plus family of calculators. A version of *Catalog Help* has been written for TI-83 Plus models that do not accept flash apps, a nice legal addition for a student with an older calculator. The TI-89 is an approved calculator with a menu-driven screen that does not require students to remember the variable order. Thus the 89's functionality provides a good benchmark for the kind of improvements that would be legal. Another specific upgrade that teachers could use is a chi-square goodness-of-fit test. The 89 includes such a feature, as does the latest operating system for the 84 Plus, so a program that performs that test would be legal.

For those using the TI-86, Texas Instruments has written an add-on program that gives it full statistics capabilities. This program simply gives it the same functions as the 83, 83 Plus, 84 Plus, and 89. Some teachers have written programs for the 86 that add other missing features: a normal probability plot, a residual list generator, a *Catalog Help*-like program, and so on. These programs are allowable.

A feature that is not included on any legal calculator is any reminder of the conditions required to perform a hypothesis test or confidence interval. Students struggle with memorizing these conditions. Some programs warn students if the conditions have been violated (i.e., "**Warning! Expecteds are less than 5!**"). As no allowable calculator offers such warnings, a program that does this would not be allowed. I have seen some teacher-made programs that ask students a series of questions to check the conditions before they run the test or interval. These also would not be allowed.

A company called Cedo Publishers offers a complete statistical package for the entire family of Texas Instruments calculators.

The selling point for the Cedo package is that it offers identical keystrokes for a classroom with a mixture of different calculators. All statistical functions are menu driven. The beginning menu offers these choices:

- Distributions
- Description
- Inference
- Regression
- Utilities

## Menus

The Distribution menu offers normal, *t*, Ç^{2}, binomial, and geometric distributions. Each distribution begins with a setup command, where the initial parameters are entered, say, µ, Ã, *n*, or *p*. Then students can choose calculations, followed by a graph with shading, if they want. Most of these features simply mirror the 89's menu-driven features. The only features that seem to enter a gray area for the AP Exam are the very slick binomial and geometric PDF histogram features. For example, once students have entered *n* and *p*, they are just one menu selection away from creating a binomial PDF graph. While any calculator allows students to enter binomial values and probabilities into two lists and then graph by correctly defining a histogram, no calculator has a feature that will do this with one command. The Distribution menu also includes inverse function commands, so the much-requested inverse-*t* command is no longer a problem.

The Description menu offers many standard features: boxplots, number summaries, and normal probability plots. It inextricably titles its histogram feature "dotplots." The dotplot feature makes histograms most of the time, but if you choose a bin width that is too small, the feature draws line graphs instead of bins. Again, Cedo offers some features that enter a gray area for the exam. One command converts data with a frequency list into a single data list. Another command tells the user what percentage of a set of data is one, two, and three standard deviations from the mean (you can compare these percentages to 68-95-99.7). Still another command superimposes a normal curve on top of a histogram to analyze normality even further. These commands are all avenues to some great calculator explorations and lessons, but they probably fall outside the boundaries of what the College Board policy allows.

The Inference menu offers a choice of intervals, tests, or sample size. The intervals and tests include one- and two-sample *z*- and *t*-procedures for means and *z*-procedures for proportions and Ç^{2}. The sample-size commands calculate the sample size required for a given margin of error. Again, these command would not be allowed on the AP Exam. Cedo also provides warnings if the expected values are too small or if the sample size is too small for a *z*-test. As discussed above, these warnings are inappropriate.

The Regression menu includes scatterplots, regression, inference for slope, residuals, and a prediction function. All of these features are standard except for the prediction choice. This feature takes a given number and evaluates it in the regression equation, giving the user the appropriate prediction. The Utilities menu offers memory and decimal place (Fix) adjustments, as well as the standard host of simulation features: random, integer, binomial, and normal.

The Cedo package presents an interesting challenge to AP Statistics teachers. For a classroom with a variety of calculators, it offers a uniform, menu-driven format that is appealing. Yet the list of functions that are not appropriate for the AP Exam is a real challenge. Each menu command runs from its own subprogram, so you could disable certain commands by installing only some of the 38 subprograms. For example, if you did not install the program ZRSIZ.8x, then any attempt to calculate sample size would simply give an error message. However, warnings about conditions for inference offer a tougher problem because they are programmed into the inference commands. Conceivably, a teacher might consider installing only the distribution features, because students experience the most frustration memorizing those parameter inputs. It would be difficult to use the full program all year and then deprive students of that tool just before exam day.

In short, you should feel encouraged to familiarize yourself with the various allowed calculators before you set out to add a new program to your students' calculators. If you can find the feature on another calculator, feel free to add the program. If not, steer clear.

*Jared Derksen has taught mathematics since 1991. During that time he has taught at levels ranging from seventh grade through college. He began teaching at Rancho Cucamonga High School in 1996 and started the AP Statistics program there. Derksen was an AP Statistics Reader in 2004 and 2005.*

## Authored by

**Jared Derksen**

Rancho Cucamonga High School

Rancho Cucamonga, California