Finding the Standard Deviation and Variance with a TI-83 Plue/TI-84

Content:  This page gives detailed instructions for finding the standard deviation and variance with a TI-83 Plus & TI-84

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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 L1 as described under Entering Data immediately above.
d1) Press STAT, move the cursor to CALC, and press ENTER. The expression “1-Var Stats”
should be pasted to the home screen. If the data is in L1, just press ENTER, otherwise
press 2nd and the list number where the data is stored and then press ENTER.  The standard
deviation and several other statistics will be displayed.
d2)  For the newer TI-84 a Stats Wizard will appear. Opposite List:, press 2ND, L1.  Delete anything opposite
FreqList:, move the cursor to Calculate and press ENTER.

e)  To calculate  the variance, merely re-enter the value for the  standard deviation, Sx  ,
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 Sx and
square that value.  If you don't like entering long numbers, you can do this:  Press VARS, 5, 3, ENTER, x2 ,
ENTER.

B.  Calculating  Numbers to Plug into a Computation Formula::

The standard deviation can be found easily by using 1-Var 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 TI-82, TI-83 Plus, or TI-84 for doing much
of the arithmetic required and obtaining numbers to plug into the formulas.
Suppose that students did sit-ups according the Figure 1 shown below.

 Student Sit-ups (x)  in (L1) x2 in    (L2) 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 Σx²=7492

Figure 1:  Completed table.

The variance computation formula is as follows:   s2 = [(Σx² -(Σx)²)/n)]/(n-1), where s2 is the variance .
So,  we will need x2 ,  ∑x2 and ∑x to plug into the formula.

a)  Enter the data in list L1 using the keystrokes indicated previously in this document

b) Press STAT, move the cursor to CALC, and press ENTER. The expression “1-Var Stats”
should be pasted to the home screen. If the data is in L1, just press ENTER, otherwise
press 2nd and the list number where the data is stored.
c)  Copy n=7, ∑x = 216, and ∑x2 =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 x2 column.   Place the cursor on the title L2, press 2nd, L1, x2, ENTER.  The squares of the
numbers in L1 will be displayed in L2.  You can enter into your table  the numbers that you found for n, ∑x, and
∑x² from the 1-Var 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
(7492-2162/7)/(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 L2 as indicated in
Figure 2 below.
(2)  Press 2ND, L1 and the screen should appear as in Figure 2. Figure 2. Multiplying list L1 and
storing in L2.

(3)  Press ENTER and the squared values will appear in list L2.
g)  You can now calculate the Σx by first placing the cursor after the last entry in L1.  Now press 2ND, List, move the cursor
to MATH and press 5 for sum(.
h) Press 2ND, L1,  ENTER and the sum will appear at the bottom of the list in L1..
i) Do the same thing for list L2 to get (Σx)2 .  The completed table is show in Figure 3 below. Figure 3.  Completed lists with
sums entered.

j)  Enter
enter (7492-2162/7)/(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 