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 August 27th, 2017, 06:00 AM #1 Member   Joined: Nov 2016 From: USA Posts: 36 Thanks: 1 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 06:07 AM. August 27th, 2017, 07:32 AM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 3,002 Thanks: 1588 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 Thanks from Seventy7 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 n-1). You can find the difference while comparing the population and sample standard deviation formulas. Thanks from Seventy7 November 7th, 2017, 01:35 PM #4 Global Moderator   Joined: May 2007 Posts: 6,807 Thanks: 717 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. Thanks from Seventy7 November 22nd, 2017, 05:27 PM #5 Senior Member   Joined: Oct 2013 From: New York, USA Posts: 661 Thanks: 87 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). Thanks from Seventy7 Last edited by EvanJ; November 22nd, 2017 at 05:31 PM. Tags answers, calculation, calculator, hand, problem, ti84 Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post CoarxFlow Math Software 5 August 26th, 2016 08:37 PM EvanJ Calculus 3 September 29th, 2015 09:48 AM plasticman99 Math Software 1 May 26th, 2015 03:29 AM Zman15 Elementary Math 3 March 27th, 2015 11:52 AM Shen Elementary Math 7 June 6th, 2014 02:59 PM

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