AP Stats on the TI-84: Every command you need for the exam

The TI-84 Plus is the most commonly used calculator on the AP (Advanced Placement) Statistics exam. CollegeBoard allows any graphing calculator on the approved list, and the Bluebook testing app also has a built-in Desmos graphing calculator, but the TI-84 Plus (and the CE variant) has the biggest install base in US high schools and the largest stock of shared tutorials. Every command you need for the exam lives in three menus: STAT, DISTR, and MATRIX.

This guide walks through the specific TI-84 commands the exam tests, keystroke by keystroke, with a worked example for each. If you'd rather see the underlying stats content, Cognito's AP Statistics past papers have every recent released paper with worked solutions.

Enter data first. STAT > EDIT gives you L1, L2, etc. Type values into L1 for one-variable data; L1 and L2 for two-variable.

1-Var Stats: STAT > CALC > 1:1-Var Stats > choose L1. Returns mean (x-bar), sample standard deviation (Sx, with n-1), population standard deviation (sigma-x, with n), median, quartiles, and n. On the exam, always use Sx (n-1), not sigma-x, unless the question explicitly says you have the whole population.

LinReg(a+bx): STAT > CALC > 8:LinReg(a+bx) > choose L1, L2. Returns the intercept (a), slope (b), correlation coefficient (r), and r-squared. To display r you have to have DiagnosticOn enabled (CATALOG, or 2ND 0, scroll to DiagnosticOn, ENTER). Do that once at the start of the year and it stays on.

Worked example: study hours L1 = {1, 2, 3, 4, 5}, test score L2 = {60, 65, 70, 80, 85}. 1-Var Stats on L1: x-bar = 3, Sx = 1.58. On L2: y-bar = 72, Sy = 10.4. LinReg(a+bx) L1, L2: a = 52.5, b = 6.5, r = 0.991, r-squared = 0.983. Regression line: y-hat = 52.5 + 6.5x.

normalcdf(lower, upper, mu, sigma): 2ND VARS (DISTR) > 2:normalcdf. Returns the probability that a Normal variable falls in a range. For the standard Normal, omit mu and sigma (defaults are 0 and 1).

Worked example: adult heights are Normally distributed with mu = 68 inches and sigma = 3. Probability an adult is between 65 and 72 inches: normalcdf(65, 72, 68, 3) returns 0.7501. Or equivalently, in z-scores: normalcdf(-1, 1.333) returns about the same value (0.7501).

invNorm(area, mu, sigma): 2ND VARS > 3:invNorm. Returns the z-score (or raw value) with a given area to the left. Useful for finding cutoffs.

Worked example: what height cuts off the top 5 percent of adults? invNorm(0.95, 68, 3) returns 72.93 inches.

binompdf and binomcdf: 2ND VARS > A:binompdf gives P(X = k) for a binomial; B:binomcdf gives P(X less than or equal to k). Arguments are (n, p, k). For P(X greater than or equal to k), use 1 minus binomcdf(n, p, k-1).

Every inference procedure has a menu entry at STAT > TESTS. The exam allows and expects you to use them; the FRQ rubric still wants you to identify the procedure (by name or by formula) and report the key values alongside the calculator output.

Worked example (one-sample t-test): a company claims bulbs last 1,000 hours. Sample of 20 bulbs has x-bar = 985, s = 40. Test H0: mu = 1000 vs Ha: mu less than 1000.

STAT > TESTS > 2:T-Test. Choose 'Stats' input. Enter mu0 = 1000, x-bar = 985, Sx = 40, n = 20, and select mu less than mu0 for the alternative. Calculate. Returns t = -1.677, p = 0.0550, df = 19. Because p greater than 0.05, we fail to reject H0.

Worked example (matched pairs): to test whether a study method improves scores, 10 students take a test before and after. Enter differences (after minus before) into L1. Run STAT > TESTS > 2:T-Test on L1 with mu0 = 0 and mu > mu0. That's a one-sample t on the differences, which is what a matched-pairs test IS.

For chi-square tests of independence or homogeneity, enter the observed counts as a matrix. 2ND MATRIX > EDIT > [A]. Set dimensions (rows x columns), then enter counts.

Then STAT > TESTS > C:chi-squared-Test. Observed = [A]. Expected: the calculator computes and stores in [B]; you don't need to enter it manually. Calculate returns chi-squared, p-value, and df.

After running the test, view [B] to see the expected counts (2ND MATRIX > 2:[B]). Check that no expected count is less than 5; if any are, the chi-square approximation is questionable and you should note this on the FRQ.