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August 27th, 2017, 07:00 AM   #1
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TI-84 calculator VS. hand calculation: why different answers to same problem?

If you have a TI-84 model calculator, then maybe you can figure out or explain what is causing the difference in answer when solving it by hand VS. calculator.

I am finding the standard deviation of five numbers:
20, 22, 24, 26, 28

The mean of these five numbers is (120/5) = 24

Using the formula by hand, I get:

SQRT [(20-24)^2+(22-24)^2+(24-24)^2+(26-24)^2+(28-24)^2)/5]
SQRT [(16+4+0+4+16)/5]
=SQRT [40/5]
=SQRT 8
=2.83

However, using the TI-84 PLUS calculator I get the answer of 3.16.

Here is what I found online on how to calculate standard deviation on the TI-84 PLUS:

2ND LIST
Tab across to select MATH
#7 STD DEV

StdDev({20,22,24,26,28}) ENTER
Answer = 3.16

I think what the TI-84 is doing is subtracting 1 from the denominator, using 4 instead of 5.
SQRT (40/4)
=SQRT(10)
=3.16

What is going on with my calculation on the TI-84 calculator?

Last edited by Seventy7; August 27th, 2017 at 07:07 AM.
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August 27th, 2017, 08:32 AM   #2
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The TI84 is calculating the sample standard deviation.

see explanation at this link ...

math.stackexchange.com/questions/15098/sample-standard-deviation-vs-population-standard-deviation
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November 7th, 2017, 11:09 AM   #3
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skeeter is right.

The difference is in the denominator (N or n-1).

You can find the difference while comparing the population and sample standard deviation formulas.
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November 7th, 2017, 02:35 PM   #4
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When using a sample mean, the sample variance formula uses n-1, so that the mathematical expectation of the sample variance is the true variance.
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November 22nd, 2017, 06:27 PM   #5
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What Seventy7 found online is not ideal. To calculate standard deviations with a TI-84 Plus, enter the numbers in a statistics list. Then push "STAT," go right to "CALC," and push 1 or enter (since 1 will be selected without moving up or down) for "1-Var Stats." It will give the sample standard deviation (Sx) and population standard deviation (a symbol I don't know how to type in front of x).

Last edited by EvanJ; November 22nd, 2017 at 06:31 PM.
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