Finding the Standard Deviation and Variance with a TI83 Plue/TI84
Content: This page gives detailed instructions for finding the standard deviation and variance with a TI83 Plus & TI84
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© 2011 Frank Kizer
Finding the Standard Deviation and Variance of Ungrouped Data:
A. Calculated Using only
the Calculator:
a) Entering Data:
1) Press STAT; then ENTER. Tables for entering data will appear. If
you need to clear a
list, move the cursor up to highlight the list name; then press
CLEAR, ENTER.
2) To enter data, just place the cursor where you want to enter the
data and press the
correct numbers, then press ENTER. You don't have to erase old
data if there is
already data in the list, but if the old list is longer than the
new list, you will need to
delete the remaining old data items. Just place the cursor over
the data and press
DEL.
b) Suppose that you have the sample of data listed immediately below and
you want to find
the standard deviation and variance.
Data: 22, 27, 15, 35, 30, 52, 35
c) Enter the data in list L_{1}
as described under Entering Data immediately above.
d_{1}) Press STAT, move the cursor to CALC, and press ENTER. The expression
“1Var Stats”
should be pasted to the home screen. If the data is in L_{1},
just press ENTER, otherwise
press 2^{nd} and the list number where the data is stored
and then press ENTER. The standard
deviation and
several other statistics will be displayed.
d_{2}) For the newer TI84 a Stats
Wizard will appear. Opposite List:, press 2ND, L_{1}. Delete
anything opposite
FreqList:,
move the cursor to Calculate and press ENTER.
e) To calculate the
variance, merely reenter the value for the standard deviation,
S_{x}^{ } ,
and square it^{, } Note: If you round off the standard deviation, you
may have a slightly different answer than
you would if you had calculated the variance separately by hand. To avoid that,
enter all decimal places for S_{x} and
square that value. If you don't like entering long numbers, you
can do this: Press VARS, 5, 3, ENTER, x^{2} ,
ENTER.
B. Calculating
Numbers to Plug into a Computation Formula::
The standard deviation can be found easily by using 1Var
Stats as described above, but
many teachers require that students do the
calculations themselves to learn
the details of the
process. The following gives a method for using the TI82, TI83 Plus, or
TI84 for doing much
of the arithmetic required and obtaining numbers to plug into the formulas.
Suppose that students did situps according the Figure
1 shown below.
Student 
Situps (x) in (L_{1}) 
x^{2} in ^{(}L_{2}) 
1 
22 
484 
2 
27 
729 
3 
15 
225 
4 
35 
1225 
5 
30 
900 
6 
52 
2704 
7 
35 
1225 



n=7 
Σx=216 
Σx˛=7492 
Figure 1: Completed table.
The variance
computation formula is as follows: s^{2} =
[(Σx˛ (Σx)˛)/n)]/(n1), where s^{2} is the variance .
So, we will
need x^{2} , ∑x^{2} and ∑x to plug into the formula.
a)
Enter the data in list L_{1} using the keystrokes indicated previously in this document.
b) Press STAT, move the cursor to CALC, and press ENTER. The
expression “1Var Stats”
should be pasted to the home screen. If the data is in L_{1}, just
press ENTER, otherwise
press 2^{nd} and the list number where the data is stored.
c) Copy n=7, ∑x = 216, and ∑x^{2} =7492
and Sx = 11.73923.
NOTE: You now have enough data to plug into the formula and solve for the
variance and standard deviation.
If you are not required to show the detailed
calculations, skip to filling in the formula in step “f.” Otherwise, continue
with the next step.
d) Now we’ll need an x^{2} column. Place the cursor on
the title L_{2}, press 2^{nd}, L_{1},
x^{2}, ENTER. The squares of the
numbers in L_{1}
will be displayed in L_{2}. You can enter into your table
the numbers that you found for n, ∑x, and
∑x˛ from the 1Var Stats
function.
e) Now, we want to use the numbers that we
previously recorded to plug into the variance formula. So, from the
home screen enter
(7492216^{2}/7)/(6). This is the variance. To
get the standard deviation from that, pess 2ND,
√, 2nd Ans.
You will have √(Ans) on your calculator. Press Enter to get the standard
deviation.
Calculating the values
f) If your teacher requires that you fill in all
of the values, you will need to complete the table as in Figure 2. Do that
as follows:
(1) Press STAT, ENTER to go the
lists if you are not already there. Place the cursor on the title of list
L_{2} as indicated in
Figure 2 below.
(2) Press 2ND, L_{1}
and the screen should appear as in Figure 2.
Figure 2. Multiplying list L_{1} and
storing in L_{2}.
(3) Press ENTER and the squared
values will appear in list L_{2}.
g) You can now calculate the Σx by first placing
the cursor after the last entry in L_{1}. Now press 2ND, List,
move the cursor
to MATH and press 5
for sum(.
h) Press 2ND, L_{1}, ENTER and the sum will
appear at the bottom of the list in L_{1}..
i) Do the same thing for list L_{2} to get
(Σx)^{2} . The completed table is show in Figure 3 below.
Figure 3. Completed lists with
sums entered.
j) Enter enter
(7492216^{2}/7)/(6) from the home screen to calculate the
variance. To find the standard deviation, press
2ND, √ , 2ND, Ans, ENTER,
or you can just record the standard deviation that and
you recorded above. In either case,
you will have 11.73...
Released:
3/15/11
Last Revised: 3/15/11