Stats without Tears
TI-83/84 Cheat Sheet

Sampling

Seeding the Random Numbers

Pick a number haphazardly and type it into the calculator, then [STO] and [MATH] » PROB » rand.

Details: Seeding the Random-Number Generator in Chapter 1.

Taking a Random Sample

randInt(1,SizeOfPopulation), then press [ENTER] until you have as many distinct numbers as you need for your sample, ignoring duplicates.

Details: Selecting Members of the Sample in Chapter 1.

Taking a Systematic Sample

Pick a number k, where you’ll be taking data from every kth individual. Then randInt(1,k) using your chosen number k.

Details: Taking a Systematic Sample in Chapter 1.

Statistics of a Sample or Parameters of a Population

For all of these, remember to use σ or s based on whether you have the whole population or just a sample.

Stats of a Plain List of Numbers

Enter numbers in L1, then 1-VarStats L1. Check n before you look at anything else.

Details: from a List of Numbers in Chapter 3.

Stats of an Ungrouped Distribution of Numbers with Frequencies

Enter the values in L1 and the frequencies in L2, then 1-VarStats L1,L2. Check n before you look at anything else.

Details: from an Ungrouped Distribution in Chapter 3.

Weighted Average

Enter the values in L1 and the weights in L2, then 1-VarStats L1,L2. Check n before you look at anything else — it should equal the total of the weights.

Details: Weighted Average in Chapter 3.

Stats of a Grouped Distribution of Number Ranges with Frequencies

Find class midpoints and enter them in L1; enter frequencies in L2. 1-VarStats L1,L2. Before looking at anything else, verify that n is total sample size, not number of classes.

Details: from a Grouped Distribution in Chapter 3.

Caution: If classes are 100–199, 200–299, …, then class midpoints are 150, 250, … (not 149.5, 249.5, …).

Five-Number Summary

Use the procedure for stats of a plain list of numbers or an ungrouped distribution of Numbers with Frequencies, above. Scroll down to the second screen.

Caution: The five-number summary is not meaningful with a grouped distribution.

Box-Whisker Diagram a/k/a Boxplot

Enter the numbers in one list. If you have frequencies, enter them in a second list. Use MATH200A Program part 2. If you don’t have the program, see Box-Whisker Plots on TI-83/84.

Details: Box-Whisker Diagrams in Chapter 3.

Caution: The boxplot is not meaningful with a grouped distribution.

Correlation and Regression

Scatterplot

x’s in L1, y’s in L2. Turn off all plots on the [Y=] screen, then [2nd Y= makes STAT PLOT] [1] [ENTER] [▼] [ENTER]. Specify lists and the mark for plotting, then [ZOOM] [9].

Details: Step 1. Make the Scatterplot in Chapter 4.

Find r, R², and Line of Best Fit

Have x’s in L1 and y’s in L2. LinReg(ax+b) L1,L2,Y1.

Details: Step 2. Perform the Regression in Chapter 4.

Note: The first time only, you must set up the calculator before doing LinReg(ax+b). Here’s how: [2nd 0 makes CATALOG] [x-1], scroll down to DiagnosticOn, and press [ENTER] twice.

Details: Step 0. Setup in Chapter 4.

Show the Regression Line

Press [GRAPH].

Predict Average y for an x

After doing the regression, press [TRACE] [▼], enter the x number, and press [ENTER].

Details: Method 1: Trace on the Regression Line Graph in Chapter 4.

Plot the Residuals (optional)

Details: Optional: Display the Residuals in Chapter 4.

Discrete Probability Distributions

Mean and SD of a Discrete PD

Values in L1, probabilities in L2. 1-VarStats L1,L2. Verify that n is exactly 1 and Sx is blank.

Details: Mean and Standard Deviation of a DPD in Chapter 6.

Caution: For geometric and binomial models you can’t use 1-VarStats but must use the formulas.

Probabilities of Geometric Distribution

Probability that the first success comes on trial number x is geometpdf(p,x).

Probability that the first success comes within the first x trials is geometcdf(p,x).

Details: Computing Probabilities in Chapter 6.

Probabilities of Binomial Distribution

Use MATH200A Program part 3. If you don’t have the program, then:

• Probability of exactly x successes in n trials is binompdf(n,p,x).
• Probability of 0 to b successes in n trials is binomcdf(n,p,b).
• Probability of a to b successes in n trials is binomcdf(n,p,b)−binomcdf(n,p,a−1).

Details: Computing Probabilities in Chapter 6.

Normal Distribution

Have Boundary(ies), Need Probability or Area

• Have left boundary only? normalcdf(LeftBoundary,10^99,Mean,SD)
• Have right boundary only? normalcdf(-10^99,RightBoundary,Mean,SD)
• Have both boundaries? normalcdf(LeftBoundary,RightBoundary,Mean,SD)

For standard ND, either specify Mean=0 and SD=1 or just omit them.

Details: From Boundaries, Find Probability in Chapter 7.

Have Probability or Area, Need Boundary(ies)

• Have area of left tail? invNorm(AreaToLeft,Mean,SD)
• Have area of right tail? invNorm(1-AreaToRight,Mean,SD)
• Have area of middle? Subtract from 1 to get area of two tails, divide by 2 to get area of one tail. Left boundary is invNorm(AreaOfOneTail,Mean,SD) and right boundary is invNorm(1-AreaOfOneTail,Mean,SD)

For standard ND, either specify Mean=0 and SD=1 or just omit them.

Details: From Probability, Find Boundaries in Chapter 7.

Does a Data Set Fit the Normal Model?

Enter the points in a list and use MATH200A Program part 4. If you don’t have the program, see Normality Check on TI-83/84.

Details: Checking Data Sets in Chapter 7.

Sampling Distribution of the Mean

Probability of getting a sample mean between LeftBoundary and RightBoundary is normalcdf(LeftBoundary,RightBoundary,Mean,SD/√SampleSize).

Details: Example 1: Bank Deposits in Chapter 8.

Sampling Distribution of the Proportion

Compute standard error as √(p*(1-p)/n) [STO→] [x,T,θ,n]. Then probability of getting a sample proportion between LeftBoundary and RightBoundary is normalcdf(LeftBoundary,RightBoundary,p,[x,T,θ,n]).

Details: Example 5: Swain v. Alabama in Chapter 8.

Confidence Intervals, Hypothesis Tests, Sample Size

See Inferential Statistics: Basic Cases.