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# Stats without TearsTI-83/84 Cheat Sheet

Updated 17 Nov 2020

Summary:

In this course, you used a lot of calculator procedures. This cheat sheet brings them all together. You’ll find just the key points here, but each section links back to the original full discussion, complete with screen shots.

(You can use any lists, not just L1 and L2.)

## 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.

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### 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.

## What’s New?

• 17 Nov 2020: Converted from HTML 4.01 to HTM5, and italicized variable names.
• (intervening changes suppressed)
• 3 Jan 2015: New article.
Because this textbook helps you,