Calculating Variance using
the TI 83+ or TI 84+
To be used to instruct in the
use of the Texas Instruments
calculators for Chapter 16
1
Example:
computer problem, pp. 371-72
• First, 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 table
• Finally, we will use the values and the
probabilities in the table to enter into
the TI 83+ (or TI 84+, if that’s what
you have).
2
Moving from tree diagram to
table
P(X)
x
Outcome
0.057
1000 2 refurbs
0.2095
+
0.2095
=
0.419
0.524
100
1 refurb
0
0 refurb
3
Where we’re going to put the
data on the TI calculators
List 2
P(X)
x
Outcome
0.057
1000
2 refurbs
0.2095+
0.2095=
0.419
0.524
100
1 refurb
0
0 refurb
List 1
4
Before you begin……
• Make 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 go
• I 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. You’re going to place
x in List1 and P(X) in List 2.
a. Enter STAT and choose EDIT, then press ENTER. This takes
you to the Lists. Use the cursor keys to go to L1.
b. 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.
c. 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.
d. 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!
6
Step 2: calculate!
a. With the 2 lists now entered, you can
do the calculation. Press the STAT key.
b. 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.
c. Choose 1-Var Stats (the “1:” will be
highlighted) and press the ENTER key.
7
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 3
8
Step 3:
Linking 1-Var Stats to the lists
Here, you will be typing in L1, L2.
a. 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 “1Var Stats”
b. Press the comma (“,) key which just above the 7
key. Your display should now look like “1-Var
Stats L1, “
c. 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”
9
Step 4:
Press ENTER key to get the following
screen
This is the expected value
of the random variable,
aka the mean (μ)
1-Var Stats
_
x =98.9
This is the standard
∑x=98.9
deviation the
∑x2=61190
problems ask for in
S x=
Chapter 16
σx=226.7350657
n=1 (except that there’s a little downward
arrow in front of the “n”)
10
Use this procedure to calculate
standard deviations
• Remember that you have to create a
table of the probability model before
you can run the calculations
• Although this procedure will calculate
the expected value (aka the mean
[μ]), the AP exam may well ask you
to show the calculations.
• Good luck!
</end of slide show>
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