Calculating Variance using the TI 83+ or TI 84+

Calculating Variance using the TI 83+ or TI 84+To be used to instruct in the use of the Texas Instruments calculators for Chapter 161Example:computer problem, pp. 371-72First, we will generate the tree diagram found on page 371.Next, we generate the table found on p. 372 by showing where the probabilities from the tree diagram fall into the columns of the tableFinally, we will use the values and the probabilities in the table to enter into the TI 83+ (or TI 84+, if thats what you have).2

Moving from tree diagram to tableP(X)xOutcome0.05710002 refurbs0.2095+0.2095=0.4191001 refurb0.52400 refurb

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Where were going to put the data on the TI calculatorsP(X)xOutcome0.05710002 refurbs0.2095+0.2095=0.4191001 refurb0.52400 refurbList 2List 1

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Before you beginMake sure you have before you the table on the previous slide (also on p.372 of the text)You have your TI 83+ or TI 84+ turned on and ready to goI will give you step-by-step instructions. You need not write them down, since this PowerPoint will be on the school web site.Run through the slides again if you have problems.5

Step 1:Look at the table. Youre going to place x in List1 and P(X) in List 2.

Enter STAT and choose EDIT, then press ENTER. This takes you to the Lists. Use the cursor keys to go to L1.Enter 1,000 for L1(1); 100 for L1(2), and 0 for L1(3). Move down the list either by using the cursor keys or by hitting the ENTER key.Move to L2 (i.e., List 2) by using the cursor keys. Go to the first entry for List 2, denominated as L2(1). Enter either the decimal equivalents listed in the table, or enter the fractional probabilities or multiplication of fractions from the tree diagram.Be absolutely sure that you have listed the probabilities in the same order as you listed the outcomes/values. If L1(1)= 1000, you MUST have 0.057 in L2(1). FAILURE TO FOLLOW THIS WARNING WILL RESULT IN DISASTER!

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Step 2: calculate!With the 2 lists now entered, you can do the calculation. Press the STAT key. After you press it, you will see, across the top of the screen, 3 menu items: EDIT, CALC, and TEST. Use the cursor keys to get to CALC menu, and a series of new items will appear. Choose 1-Var Stats (the 1: will be highlighted) and press the ENTER key.

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What your calculator should look like now:Your calculator display should now look like this: 1-Var Stats followed by a flashing rectangular cursor. Move on to the next slide to follow the instructions for step 38

Step 3: Linking 1-Var Stats to the listsHere, you will be typing in L1, L2.First, depress the yellow 2nd key in the upper left of the calculator, followed by the 1 key on the keypad. If you have correctly pushed those in order, L1 will appear on the calculator after 1-Var StatsPress the comma (,) key which just above the 7 key. Your display should now look like 1-Var Stats L1, Press the 2nd key (see step 3(b) above), followed by the 2 key, which inserts L2. Your display should now look like this: 1-Var Stats L1, L2

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Step 4:Press ENTER key to get the following screen 1-Var Stats _ x =98.9 x=98.9 x2=61190 Sx= x=226.7350657n=1 (except that theres a little downward arrow in front of the n)

This is the standard deviation the problems ask for in Chapter 16This is the expected value of the random variable, aka the mean ()10

Use this procedure to calculate standard deviationsRemember that you have to create a table of the probability model before you can run the calculationsAlthough this procedure will calculate the expected value (aka the mean []), the AP exam may well ask you to show the calculations.Good luck!

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