TI-84 Calculator Guide for AP Statistics

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Chapter 0 · Foundations

Getting Started — Know Your Calculator

Before diving into statistics, understand how the TI-84 is organized. The key layout follows a logical color-coded system that tells you exactly what each button does and how to access hidden functions.

The Color-Code System

⬛ Black Keys

Primary functions — what you see printed directly on the key. These are the standard operations you use most often.

🟡 2nd Key (Yellow)

Unlocks the function printed above each key in yellow. Press 2nd first, then the key. Example: 2nd + LIST = STAT PLOT.

🔵 ALPHA Key (Green)

Lets you type letters (A–Z) and access functions printed in green above each key. Used for naming lists and storing variables.

↩ ENTER Key

Executes commands, confirms selections, and moves to the next entry. Think of it as the "Go" button for every operation.

Critical Keys for AP Statistics

①

STAT — Your Most-Used Key

Opens the Statistics menu with EDIT (for data), CALC (for calculations), and TESTS (for inference). You'll press this dozens of times on the AP exam.

②

2nd + VARS = DISTR

Opens the Distribution menu — where you find normalcdf, invNorm, tcdf, χ²cdf, and all probability functions. Memorize this combo!

③

2nd + Y= = STAT PLOT

Controls the graphing plots. You'll use this to set up histograms, scatterplots, and box-and-whisker plots from your data lists.

④

2nd + STAT = LIST

Access the LIST menu to see all stored lists (L1–L6), and use operations like sum( and mean( directly on lists.

How to Reset the Calculator

⚠️ On the AP exam, a proctor may ask you to clear your calculator. Know how to do this without losing all your settings!

1

Clear RAM (All Memory)

2nd→+→7 (Reset)→1 (All RAM)→2 (Reset)

This wipes lists, programs, and stored values. Use when told to reset.

2

Turn Diagnostics ON (Must Do After Reset!)

After any reset, run this to enable r and r² in regression output:

2nd0

Scroll down to DiagnosticOn and press ENTER ENTER

📋

Chapter 1 · Data Entry

Entering & Managing Data in Lists

All statistics on the TI-84 start with data in lists (L1 through L6). Think of these as columns in a spreadsheet. Learning to enter, edit, and manage list data efficiently is the foundation of everything else.

Opening the List Editor

1

Press STAT → EDIT

STAT→1: Edit→ENTER

You'll see a spreadsheet with columns L1, L2, L3... The cursor is at the top of L1.

2

Type your data values

Type each number and press ENTER to move down. Use the arrow keys to move between lists. To enter negative numbers, use the (-) key (NOT the minus sign).

3

Navigate between lists

Press ▶ to go to L2, ◀ to go back to L1. Use ▲ ▼ arrows to move between rows. For L4–L6, keep pressing ▶.

📘 Example: Enter the dataset {12, 15, 18, 22, 9, 17}

L1 L2 L3
12 ------- -------
15
18
22
9
17
---
L1(7)=_

Clearing a List

A

Method 1: Arrow up to the List Name

Move the cursor to the top until the list name (L1) is highlighted. Then press CLEAR then ENTER. This empties the whole list instantly.

B

Method 2: Via STAT → ClrList

STAT→4: ClrList→2nd1(= L1)→ENTER

Use this when you want to clear a list without opening the editor.

Deleting & Inserting Values

✏

Delete a single value

Highlight the value you want to delete and press DEL. The values below shift up automatically.

+

Insert a value (push others down)

Move to where you want to insert, then press 2nd + DEL (this is INS). A blank row appears above the cursor. Type your value and press ENTER.

💡 Using L2 for Frequency: When your data is in L1 and frequencies are in L2 (like "score 85 appeared 3 times"), you can use both lists together in 1-Var Stats. This is covered in Chapter 2!

📊

Chapter 2 · Descriptive Statistics

1-Variable Statistics — Mean, Median, SD & More

The 1-Var Stats command is one of the most powerful tools for AP Statistics. One command gives you mean, standard deviation, median, quartiles, min, max, and more. Here's exactly how to use it and what each output means.

Running 1-Var Stats

1

Enter your data into L1 (see Chapter 1)

Make sure your data is already in L1 (or whichever list you'll use).

2

Go to STAT → CALC → 1-Var Stats

STAT→▶(CALC)→1: 1-Var Stats→ENTER

3

Specify your list and press ENTER

A dialog asks for "List:" and "FreqList:". For a simple single dataset in L1:

1-Var Stats
List:L1
FreqList:
Calculate

Press ENTER to Calculate.

Reading the Output — What Every Symbol Means

Symbol	Name	What It Means
x̄	Mean	The arithmetic average of all values
Σx	Sum	Total sum of all data values
Σx²	Sum of Squares	Sum of each value squared (used internally)
Sx	Sample Std Dev	⭐ Use for SAMPLES — divides by (n-1)
σx	Population Std Dev	Use for POPULATIONS only — divides by n
n	Count	Number of data values
minX	Minimum	Smallest value in the dataset
Q1	First Quartile	25th percentile — median of lower half
Med	Median	Middle value (50th percentile)
Q3	Third Quartile	75th percentile — median of upper half
maxX	Maximum	Largest value in the dataset

⚠️ Sx vs σx on the AP Exam: Almost always use Sx (sample standard deviation). You use σx only when your data IS the entire population (like all 50 US states). In AP Stats, data is almost always a sample.

Using Frequency Lists (Weighted Data)

If your data has a frequency table (e.g., "Score 80 appeared 3 times, Score 90 appeared 5 times"):

1

Put scores in L1, frequencies in L2

L1: {80, 90, 95} and L2: {3, 5, 2}

2

In 1-Var Stats dialog, set FreqList to L2

1-Var Stats
List:L1
FreqList:L2
Calculate

The calculator now weights each value correctly by its frequency.

IQR and Outlier Boundaries

Interquartile Range (IQR)

IQR = Q3 − Q1

Outlier Fences (1.5 × IQR Rule)

Lower Fence = Q1 − 1.5 × IQR
Upper Fence = Q3 + 1.5 × IQR

💡 After running 1-Var Stats, write down Q1 and Q3 from the output. Then compute IQR and the fences manually on your calculator's home screen.

📈

Chapter 3 · Visualization

Histograms, Box Plots & Scatterplots

The TI-84 can create histograms, box-and-whisker plots, and scatterplots from your list data. These visuals help you check shape, spread, outliers, and associations — all key concepts on the AP exam.

Setting Up STAT PLOT

1

Open STAT PLOT menu

2nd+Y== STAT PLOT

Select Plot1 and press ENTER.

2

Turn Plot ON and choose your plot type

Plot1 Plot2 Plot3
On Off
Type: 📊 (histogram) or 🗂 (box) or ⊡ (scatter)
Xlist: L1
Freq: 1

The icons from left to right: Scatter, Line, Histogram, Modified Box, Standard Box.

3

Press ZOOM → 9 (ZoomStat) to auto-fit

ZOOM→9: ZoomStat

ZoomStat automatically sets the window to perfectly fit your data. Always use this after setting up a plot!

Histogram — Checking Shape & Distribution

①

Select the histogram icon (3rd icon, looks like bars)

Set Xlist: L1 and Freq: 1 (or L2 if you have frequencies)

②

Press GRAPH, then use TRACE to read bars

Press TRACE and use ◀ ▶ arrows. Each bar shows: min ≤ x < max and the count (n = ) for that bar.

💡 To change bar width, adjust the WINDOW settings. Press WINDOW and change Xscl to change the bar width (class width). A good starting point is Xscl = (Max − Min) / 5.

Box-and-Whisker Plot (Boxplot)

①

Choose the Modified Boxplot icon (4th icon)

The modified boxplot shows individual outliers as dots beyond the whiskers. This is the most useful version for AP Statistics.

②

Press ZOOM → 9, then TRACE to read the 5-number summary

TRACE gives you: minX (or first outlier), Q1, Med, Q3, maxX (or last outlier). Use ◀ ▶ arrows to move between each key value.

📌 Comparing Two Datasets: Put data in L1 and L2. Turn on Plot1 with L1 and Plot2 with L2 (both as boxplots). Press ZOOM → 9 to see them stacked on the same axes — perfect for comparing distributions!

Scatterplot (for Regression Analysis)

①

Put x-values in L1, y-values in L2

Make sure each x-value and y-value are in the same row (paired data).

②

STAT PLOT → Plot1 → first icon (scatter), Xlist: L1, Ylist: L2

Set Mark to a dot or plus sign. Press ZOOM → 9 to view.

📉

Chapter 4 · Regression

Linear Regression (LinReg) & Correlation

Linear regression finds the best-fit line through your data. The TI-84 computes the equation ŷ = a + bx, the correlation coefficient r, and the coefficient of determination r² — all at once.

⚠️ First time only: You must enable DiagnosticsOn to see r and r²! Press 2nd 0 (CATALOG), scroll to DiagnosticOn, press ENTER twice.

Running Linear Regression

1

Enter data: x in L1, y in L2

Verify each pair is on the same row in the list editor.

2

STAT → CALC → 8: LinReg(a+bx)

STAT→▶(CALC)→8: LinReg(a+bx)→ENTER

3

Set the options dialog and press Calculate

LinReg(a+bx)
Xlist:L1
Ylist:L2
FreqList:
Store RegEQ:Y1
Calculate

Storing the equation in Y1 lets you graph the line over your scatterplot!

4

Read the output

LinReg
y=a+bx
a=2.341 ← y-intercept
b=0.876 ← slope
r²=0.9214 ← 92.1% variation explained
r=0.9599 ← strong positive correlation

Interpreting the Output

a (y-intercept)

Predicted value of y when x = 0. "When [x-variable] is 0, we predict [y-variable] to be a."

b (slope)

For each 1-unit increase in x, predicted y changes by b units. "For each additional [x], [y] increases/decreases by b."

r (correlation)

Ranges from -1 to +1. Measures direction and strength of linear association. |r| > 0.8 is strong.

r² (R-squared)

% of variation in y explained by x. r² = 0.92 means 92% of variability in y is explained by the linear model.

Calculating Residuals

✓

After LinReg, the RESID list is auto-generated

Go to STAT → EDIT and arrow right to an empty list. Move to the list name area and press 2nd STAT (LIST). Scroll to RESID and press ENTER. Now you have residuals in a list!

📌 Residual Plot: Put RESID in L3. Turn on Plot2 as a scatterplot with L1 on x-axis and L3 on y-axis. A random scatter (no pattern) in the residual plot confirms a linear model is appropriate.

🎲

Chapter 5 · Probability

Combinations, Permutations & Probability

The TI-84 can compute factorials, combinations (nCr), and permutations (nPr) — essential for probability calculations involving counting methods.

Factorials, nCr, nPr

!

Factorial: n!

Type the number, then press MATH → scroll to PRB → select 4:!

5!
120

C

Combinations: nCr — "n choose r"

Type n, then MATH → PRB → 3: nCr, then type r, press ENTER.

10 nCr 3
120

How many ways to choose 3 items from 10 (order doesn't matter).

P

Permutations: nPr — ordered arrangements

Type n, then MATH → PRB → 2: nPr, then type r, press ENTER.

10 nPr 3
720

How many ways to arrange 3 items from 10 (order DOES matter).

Key Formulas

nCr = n! / (r! × (n-r)!)
nPr = n! / (n-r)!
nPr = nCr × r!

Random Number Generation

🎲

Generate random integers: randInt(

MATH→▶ ▶ ▶(PRB)→5: randInt(

Format: randInt(min, max, count)
Example: randInt(1,6,10) rolls a die 10 times

randInt(1,6,10)
{3 1 5 6 2 4 1 3 6 2}

🔔

Chapter 6 · Distributions

Normal, Binomial & t-Distributions

All distribution calculations live in 2nd → VARS (DISTR). Learn to navigate this menu and you can answer nearly any probability or p-value question on the AP exam.

📌 Access all distributions via: 2nd VARS → This opens the DISTR menu.

Normal Distribution

A

normalcdf( — Finding probabilities (area under curve)

Format: normalcdf(lower, upper, μ, σ)

2ndVARS→2: normalcdf(

Example: P(65 < X < 80) where μ = 70, σ = 5

normalcdf(65, 80, 70, 5)
.8185946

💡 For "less than" problems: use -1E99 as the lower bound. For "greater than": use 1E99 as the upper bound. (Type 1 2nd , 99 for E99)

B

invNorm( — Finding the x-value from a probability

Format: invNorm(area, μ, σ, tail)

2ndVARS→3: invNorm(

Example: What score is at the 90th percentile? (μ=70, σ=5)

invNorm(0.90, 70, 5, LEFT)
76.408...

The tail option: LEFT means area is to the left (default). Use CENTER for two-tailed.

t-Distribution (for t-tests & intervals)

A

tcdf( — t-distribution probability

Format: tcdf(lower, upper, df)

2ndVARS→6: tcdf(

Example: P(t > 2.1) with df = 15 (two-tailed p-value)

tcdf(2.1, 1E99, 15)
.0267 × 2 = 0.0534

B

invT( — Finding the critical t-value

Format: invT(area to left, df)

2ndVARS→4: invT(

Example: t* for 95% CI with df = 24

invT(0.975, 24)
2.0639

(Use 0.975 for 95% CI because 2.5% is in each tail)

Binomial Distribution

A

binompdf( — Exactly k successes

Format: binompdf(n, p, k)

2ndVARS→A: binompdf(

Example: P(X = 3) with n=10, p=0.4

binompdf(10, 0.4, 3)
.2150

B

binomcdf( — At most k successes (cumulative)

Format: binomcdf(n, p, k)

2ndVARS→B: binomcdf(

Example: P(X ≤ 3) with n=10, p=0.4

binomcdf(10, 0.4, 3)
.3823

💡 For P(X ≥ k), use 1 − binomcdf(n, p, k−1)

📐

Chapter 7 · Confidence Intervals

1-Sample Z, T & Proportion Intervals

Confidence intervals are built-in to the TI-84 under STAT → TESTS. The calculator does the heavy lifting — you just need to know which test to pick, where to find your inputs, and how to report the output.

How to Access All Interval Tests

1-Prop Z-Interval (Proportion CI)

1

STAT → TESTS → A: 1-PropZInt

STAT→▶(TESTS)→A: 1-PropZInt

2

Enter x, n, and C-Level

1-PropZInt
x: 142 ← # of successes
n: 200 ← sample size
C-Level: .95 ← confidence level
Calculate

Where x = number with the characteristic, n = total sample size.

3

Read the output

1-PropZInt
(.64365, .77635)
p̂=.71
n=200

The interval is (0.644, 0.776). We're 95% confident the true proportion is between 64.4% and 77.6%.

T-Interval (Mean CI, σ unknown — most common!)

1

STAT → TESTS → 8: T-Interval

STAT→▶(TESTS)→8: TInterval

Choose Stats (if you have x̄, Sx, n) or Data (if data is in L1).

2

Using Stats input method

TInterval
Inpt: Stats Data
x̄: 78.3
Sx: 12.4
n: 35
C-Level: .90
Calculate

What the Calculator is Computing

x̄ ± t* × (Sx / √n)

Z-Interval (Mean CI, σ known)

①

STAT → TESTS → 7: ZInterval

Use this only when σ (population standard deviation) is given to you. In practice, this is rare — almost always use T-Interval.

🔬

Chapter 8 · Hypothesis Testing

One-Sample Z & T Tests

Hypothesis testing on the TI-84 computes your test statistic (z or t) AND the p-value simultaneously. All tests are under STAT → TESTS. Always state H₀ and Hₐ before touching the calculator!

The General Workflow for ANY Test

①

State hypotheses and identify the correct test

H₀: parameter = value vs. Hₐ: parameter ≠/</> value

②

Enter data or summary stati

Master the TI-84 for AP Statistics