Graphing Calculator Instructions TI-83 video tutorials are available here: (Part 1, Part 2). The Discrete Mean & Stdev link shows how to calculate a mean and stdev for a discrete random variable. The Outliers link shows how to calculate outliers using the lists. The Matrix: TI-89 link shows how to create a matrix using the TI-89 calculator for use in a Test of Independence. The Random Numbers link shows how to generate random numbers. The Sorting link shows how to sort a list. The TI-89 link gives some general instructions for the TI-89 plus linear regression instructions. Link to Graphing Calculator Help for Several TI Calculators

Calculating the Mean and Standard Deviation of a Discrete Probability Distribution on the TI-83 and TI-86 Enter the possible values for your random variable X in list L1. Enter the probabilities for each value of X in list L2 in the position next to the value of X. Calculate “One Variable Statistics” for lists L1 and L2. (Do this the same way you calculate one variable statistics for data values and frequencies when given a set of data.) The calculator will give the mean as "x-bar" x̄ although we know that this mean is actually µ because it is the mean of a probability distribution. The calculator will give the standard deviation as σ which indicates the standard deviation of a probability distribution (as well as the standard deviation of a population). The calculator does not give you a value for s because the frequencies you gave it are not whole numbers.

Outlier Instructions for the TI-83, 86, and 89 Calculators When you finish going over these instructions, do TEXT problem #5 ("stories" and "height of building") in Ch. 12. One of the points is an outlier.This explains how to find outliers on various calculators. Suppose the data is (3,5), (6,8), (9,7), (5,20). The xlist is 3, 6, 9, 5 and the ylist is 5, 8, 7, 20. Put the xlist into L1 and the ylist into L2. Do the linear regression. yhat = 11.2267 - .2133xTI-89: Use Flashapps to enter your lists and then find your instructions below the instructions for the TI-83 & 86.

For TI-83 & 86 Calculators Go back to where you entered the lists L1 and L2 and go to the list name L3. Enter 11.2267-.2133L1 (You enter the equation at the bottom of the screen where it says L3. Press Enter. In L3 are the yhat values. Arrow to the list name L4. Enter L2-L3. Press Enter. (In L4 are the y - yhat values.) Arrow to the list name L5. Enter L4^2. Press Enter. (In L5 are the (y - yhat)^2 values.) Continue by finding the Instructions for the appropriate calculator below (83 or 86):

For TI-83 Exit to the Home Screen. Clear it. Press 2nd LIST. Arrow to MATH. Press 5:sum. (Press L5). Press Enter. You should see 137.1467 (to 4 decimal places). This is the SSE. Calculate s. Press the square root symbol and enter (137.1467/2). (You get the denominator by taking the number of data points and subtracting 2: 4 - 2 = 2.) Press Enter. You should see 8.2809 (to 4 decimal places). Multiply 8.2809 by 1.9. You should see 15.7337. Press L4. Press Enter. (Use the arrow keys to scroll through the list.) Compare 15.7337 to the absolute values of the numbers in L4. If any absolute value is greater than or equal to 15.7337, then the corresponding point is an outlier. Absolute values of the numbers in L4 are 5.587, 1.947, 2.307, 9.8398. None of them are greater than 15.7337, so no point is an outlier.

For TI-86 Exit to the Home Screen. Clear it. Press 2nd LIST. Press F5 (OPS). Press MORE. Press F1 (sum). Press 2nd F3 (NAMES). Find the F key with L5 and press it. Press Enter. You should see 137.1467 (to 4 decimal places). This is the SSE. Calculate s. Press the square root symbol and enter (137.1467/2). (You get the denominator by taking the number of data points and subtracting 2: 4 - 2 = 2.) Press Enter. You should see 8.2809 (to 4 decimal places). Multiply 8.2809 by 1.9. You should see 15.7337. Press L4. Press Enter. (Use the arrow keys to scroll through L4.) Compare 15.7337 to the absolute values of the numbers in L4. If any absolute value is greater than or equal to 15.7337, then the corresponding point is an outlier. Absolute values of the numbers in L4 are 5.587, 1.947, 2.307, 9.8398. None of them are greater than 15.7337 so no point is an outlier.

For TI-89 NOTE: When you do Linear Regression, a list called "resid" is created automatically. This list has the y - yhat values in it. Go into Flashapps and into your lists. Arrow to "resid" so you see it. Then arrow to the list name L3. Press F3. Press 1:names. Arrow down to STATVARS. If it is not checked, press F4. Then arrow down to resid. Press Enter. Press ^2. L3 will have the (y - yhat)^2 values. Press HOME and Press F1 8 to clear it. Press 2nd MATH. Press 3:List. Press 6:Sum. Press alpha L3. Depending on how you have MODE Display Digits set, you should see approximately 137.1467. This is the SSE. Calculate s. (You should be HOME.) Press clear. Press the square root symbol and enter 137.1467/2). (You get the denominator by taking the number of data points and subtracting 2: 4 - 2 = 2.) Press Enter. You should see 8.2809 (to 4 decimal places). Press the times key and enter 1.9. Press Enter. You should see 15.7337 Press clear. Press 2nd VAR-LINK. Arrow down to resid (It is below STAT VARS). Press Enter. Arrow up to the list. Scroll through the list using the arrow keys. Compare 15.7337 to the absolute values of the numbers in the list. If any absolute value is greater than or equal to 15.7337, then the corresponding point is an outlier. Absolute values of the numbers in the list are approximately 5.59, 1.95, 2.31, 9.84. None of them are greater than 15.7337 so no point is an outlier.

Create a Matrix to use in a Test of Independence on the TI-89 Press APPS 6:Data/Matrix Editor Press 3:New Arrow over and down to 2:Matrix. Press Enter Arrow down to Folder. Either use the one that is there or arrow over and down to another folder name (don't use statvars) and press Enter. Arrow down to Variable and enter a name you will remember. Arrow down to Row dimension and enter the number of rows you want. Arrow down to Column dimension and enter the number of columns you want. (NOTE: You can change these numbers if you want for a different problem.) Press Enter until you see your matrix with zeroes as the entries. Fill in your matrix with the data from the table. Press APPS Press 1:Flashapps Press Enter Press F6 TESTS Press 8:Chi2 2-way Enter the name of your matrix at Observed Mat: Press Enter. You should see the screen with the test statistic and the p-value.To change the size of your matrix, press APPS 6:Matrix/Data Editor 2:Open. Then fill in the OPEN screen with Matrix, the correct folder, and the correct name of your matrix. Press Enter until you see your matrix. To resize it, press F6 Util 6:Resize Matrix. Enter the row dimension and arrow down to column dimension and enter that number. Press Enter until you see your resized matrix.

Generating Random Numbers with the TI Calculators The following functions will generate random numbers from the list of numbers 1 - 60.

TI-83 Press MATH. Arrow over to PRB. Press 5:randInt. Enter (1,60). Press Enter and you will see the first random number. Keep pressing Enter to get random numbers between 1 and 60, inclusive.

TI-86 Press 2nd MATH. Press PROB (in F2). Press randint (in F5). Enter (1,60). Press Enter and you will see the first random number. Press Enter and you will see the first random number.

TI-89 Press 2nd MATH. Press 7:Probability. Press 4:rand. Enter (1,60)and press Enter. You will see the first random number. Keep pressing Enter to get random numbers between 1 and 60, inclusive.

How to Sort Data Using the TI Calculators Only sort data where the frequencies are all 1.

TI-83 Enter the data into a list L1, L2, L3, L4, L5, or L6. Press 2nd LIST (above the STAT key). Arrow over (use the right arrow) to OPS. Press 1 (for 1:SORTA). Enter the name of your list and a right parenthesis. Press Enter. Press STAT 1 and look at your list. It should be in sorted order.

TI-86 Enter the data into a list. Press EXIT. Press 2nd LIST (above – key). Press OPS (in F5). Press sortA (in F2). Enter the list name by pressing 2nd NAMES (in M3). Arrow to your list and press the appropriate F key. Press the STO-> key. Enter the same list name. Press Enter. Check that your list is sorted by going back into 2nd STAT EDIT.

TI-89For the TI-89, get Flashapps from the TI Web site or have your instructor put it into your calculator. Press APPS 1 (for 1:Flashapps). Press Enter. Press Enter again. Enter your data into a list (Enter data into one of the L lists, L1, L2, L3, L4). Press F3 (for List). Press 2 (for 2:Ops). Press 1 (for 1:Sort List). If you see your list name, press Enter. If the correct list name is not there, then enter it. Press Enter. You should see your list in sorted order.

Notes for the TI-89 Calculator In most TI-89 calculators, you must load a new operating system first and then the APPS statistics program. You can either go to your instructor OR you can go to the TI-89 site to get the operating system and the APPS statistics program. You must go to the TI-89 site to get the Guidebook. It has all the instructions for running the statistics program.To go to the TI-89 site, click http://education.ti.com to get to the TI-89 link. Then choose "apps" and "Handheld Software Application." From this page, you can download the operating system (version 2.05) and statistics program (Statistics with List Editor - this page will have both the operating system and the program).You must then load the Advanced Mathematics Software Operating System and the Statistics with List Editor from your computer to the TI-89 calculator (unless your instructor has loaded them directly into your calculator). For that, you will need the TI-GRAPH LINK™ software and the TI-GRAPH LINK™ Cable. TI sells them on their Web Site.

Getting Started Create the folder “mystat” (for statistics): Press 2nd VAR-LINK. Press F1 Manage. Press 5:Create Folder. Enter the name “mystat” and press Enter twice. Make mystat your current folder:Press MODE. Arrow down to Current Folder and arrow over and down to mystat. Press Enter twice. You should see the name MYSTAT in the lower left corner. Creating list names L1, L2, and L3:Press APPS 1:Flashapps. Press Enter. Arrow up into the name area of the lists and over until you reach a blank title area. Press L (above the 4). Press alpha. Press 1. Press Enter. Arrow up into the name area of the lists and over until you reach a blank title area. Press L. Press alpha. Press 2. Press Enter. Arrow up into the name area of the lists and over until you reach a blank title area. Press L. Press alpha. Press 3. Press Enter.

Linear Regression Given the data set: (3, 5), (6, 8), (9,7), (5, 20). The xlist is 3, 6, 9, 5 and the ylist is 5, 8, 7, 20. Put the xlist into L1 and the ylist into L2.

Constructing a Scatter Plot Make sure you are using Flashapps (Press APPS 1:Flashapps. Press Enter.) SCATTERPLOT: After you are have entered your lists in L1 and L2, press F2. Press 1:Plot Setup. Highlight Plot 1 and make sure there are no checks next to any other plots. If there are, arrow to the plot and press F4. Then arrow back to Plot 1. Press F1: Define. For Plot Type, press the right arrow and press 1:Scatter. Arrow down, press the right arrow and press 1:Box. Arrow down to x. Press alpha L1. Arrow down to y and press alpha L2. Arrow down to Use Freq and Categories? and use the right arrow. Highlight NO and press Enter. Press Enter again. Press F5 Zoomdata. You should see the scatterplot. Press F3 to trace and the arrow keys to see the coordinates of the points.

Calculating the Regression Equation Press APPS, 1:Flashapps, and Enter. Press F4:Calc. Press 3:Regressions. Press 1:LinReg (ax+b). For x List, enter alpha L1. Arrow down. For y List, enter alpha L2. For Store RegEqn to:, arrow right and arrow down to y1(x) (or any one of the y's) and press Enter. Press Enter. You should see a screen with a, b, r^2, and r on it. The regression is complete. Write down the equation from the information and press Enter. The linear regression is yhat = 11.2267 - .2133x

Drawing the Regression Line Press the key with the green diamond on it (it is below the 2nd key) and press Y= (above the F1 key). This is the Line of Best Fit. Press the key with the green diamond on it and press GRAPH (above the F3 key). The line will be drawn.

Outliers When you do Linear Regression, a list called "resid" is created automatically. This list has the “y – yhat” values in it. Go into Flashapps and into your lists. Arrow to "resid" so you see it. Then, arrow to the list name L3. Press F3. Press 1:names. Arrow down to STATVARS. If it is not checked, press F4. Then, arrow down to resid. Press Enter. Press ^2. Press Enter. L3 will have the (y - yhat)^2 values. Press HOME and Press F1 8 to clear it. Press 2nd MATH. Press 3:List. Press 6:Sum. Press alpha (L3). Depending on how you have MODE Display Digits set, you should see approximately 137.1467. This is the SSE. Calculate s. (You should be HOME.) Press clear. Press the square root symbol and enter 137.1467/2. (You get the denominator by taking the number of data points and subtracting 2: 4 - 2 = 2.) Press Enter. You should see 8.2809 (to 4 decimal places). Press the times key and enter 1.9. Press Enter. You should see 15.7337. Press clear. Press 2nd VAR-LINK. Arrow down to resid (it is below STAT VARS). Press Enter. Press Enter again. Arrow up to the list. Scroll through the list using the arrow keys. Compare 15.7337 to the absolute values of the numbers in the list. If any absolute value is greater than or equal to 15.7337, then the corresponding point is an outlier. Absolute values of the numbers in the list are approximately 5.59, 1.95, 2.31, 9.84. None of them are greater than or equal to 15.7337. Therefore, for this data set, no point is an outlier.