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August 27th, 2017, 06:00 AM  #1 
Member Joined: Nov 2016 From: USA Posts: 33 Thanks: 1  TI84 calculator VS. hand calculation: why different answers to same problem?
If you have a TI84 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 [(2024)^2+(2224)^2+(2424)^2+(2624)^2+(2824)^2)/5] SQRT [(16+4+0+4+16)/5] =SQRT [40/5] =SQRT 8 =2.83 However, using the TI84 PLUS calculator I get the answer of 3.16. Here is what I found online on how to calculate standard deviation on the TI84 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 TI84 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 TI84 calculator? Last edited by Seventy7; August 27th, 2017 at 06:07 AM. 
August 27th, 2017, 07:32 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,755 Thanks: 1405 
The TI84 is calculating the sample standard deviation. see explanation at this link ... math.stackexchange.com/questions/15098/samplestandarddeviationvspopulationstandarddeviation 
November 7th, 2017, 10:09 AM  #3 
Newbie Joined: Oct 2017 From: US Posts: 13 Thanks: 1 
skeeter is right. The difference is in the denominator (N or n1). You can find the difference while comparing the population and sample standard deviation formulas. 
November 7th, 2017, 01:35 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,528 Thanks: 589 
When using a sample mean, the sample variance formula uses n1, so that the mathematical expectation of the sample variance is the true variance.

November 22nd, 2017, 05:27 PM  #5 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 602 Thanks: 82 
What Seventy7 found online is not ideal. To calculate standard deviations with a TI84 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 "1Var 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 05:31 PM. 

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