# stdDev on Ti-84 **URL:** \ **Category:** Factual Questions\ **Created:** [April 20, 2014, 7:57pm UTC](https://boards.straightdope.com/t/stddev-on-ti-84/686557 "2014-04-20T19:57:32Z")\ **Posts on this page:** 8\ **Page:** 1
**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\ **Post date:** [April 20, 2014, 7:57pm UTC](https://boards.straightdope.com/t/stddev-on-ti-84/686557/1 "2014-04-20T19:57:32Z")
I entered the following values into my Ti-84 calculator: stdDev({4.971e-2, 4.943e-2, 4.932e-2}) The answer was 2.0108. Given ‘s’ is standard deviation, when I do it ‘longhand’: s = sqrt(((4.971e-2 + 4.943e-2 + 4.932e-2)^2)/(3-1)), I get 0.104977 Is stdDev on the calculator RELATIVE standard deviation? ---
**Author:** ![OldGuy](https://avatars.discourse-cdn.com/v4/letter/o/3bc359/32.png) [@OldGuy](https://boards.straightdope.com/u/OldGuy)\ **Post date:** [April 20, 2014, 8:56pm UTC](https://boards.straightdope.com/t/stddev-on-ti-84/686557/2 "2014-04-20T20:56:31Z")
You need to subtract off the mean then square each difference from the mean and add not square the sum The answer might divided by 3 rather than 2 if it is calculating the population standard deviation rather than estimating from a sample standard deviation. dividing by 3 also gives the maximum likelihood estimate in a sample, though that is less used. The answers are 0.000201 and 0.000164. I cannot fathom at all what the calculator is doing. ---
**Author:** ![Jragon](https://avatars.discourse-cdn.com/v4/letter/j/e19b73/32.png) [@Jragon](https://boards.straightdope.com/u/Jragon)\ **Post date:** [April 20, 2014, 8:58pm UTC](https://boards.straightdope.com/t/stddev-on-ti-84/686557/3 "2014-04-20T20:58:10Z")
I don’t think you’re calculating stddev right. It’s the _deep breath_ square root of the sum of the square of the differences between each data point and the mean divided by the number of elements. mean(4.971e-2, 4.943e-2, 4.932e-2) = 4.949e-2 So stddev(4.971e-2, 4.943e-2, 4.932e-2) = sqrt( ((4.971e-2 - 4.949e-2)[sup]2[/sup] + (4.943e-2 - 4.949e-2)[sup]2[/sup] + (4.932e-2 - 4.949e-2)[sup]2[/sup])/3 ) ---
**Author:** ![OldGuy](https://avatars.discourse-cdn.com/v4/letter/o/3bc359/32.png) [@OldGuy](https://boards.straightdope.com/u/OldGuy)\ **Post date:** [April 20, 2014, 9:03pm UTC](https://boards.straightdope.com/t/stddev-on-ti-84/686557/4 "2014-04-20T21:03:24Z")
Actually I checked and the sample std deviation is 0.000201, so I guess you’re just misreading the calculator’s decimal point position. ---
**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\ **Post date:** [April 20, 2014, 9:32pm UTC](https://boards.straightdope.com/t/stddev-on-ti-84/686557/5 "2014-04-20T21:32:07Z")
> [@Jragon](#): > > I don’t think you’re calculating stddev right. It’s the _deep breath_ square root of the sum of the square of the differences between each data point and the mean divided by the number of elements. > > mean(4.971e-2, 4.943e-2, 4.932e-2) = 4.949e-2 > > So stddev(4.971e-2, 4.943e-2, 4.932e-2) = sqrt( ((4.971e-2 - 4.949e-2)[sup]2[/sup] + (4.943e-2 - 4.949e-2)[sup]2[/sup] + (4.932e-2 - 4.949e-2)[sup]2[/sup])/3 ) According to the printout I have (modified format for posting): > [@](#): > > The standard deviation is, > > s = sqrt((2.56_10^-4 + 2.16_10^-4 + 0.020\*10^-4)^2 / (3-1)) = 0.0154 g This is troubling, because when I use stdDev on the calculator: stdDev({2.56_10^-4,2.16_10^-4 ,0.020\*10^-4}) I get .0001366 and not 0.0154. When I do sqrt(((2.56e-4+2.16e-4+.020e-4)^2)/(3-1)) I get .0003352. So in short: [ul][li]When I use the stdDev function as I was shown how to use it, and using the given values (as opposed to the numbers in the OP), the answer is not the given answer.[/li][li]When I take the square root of the sum of the values squared and divided by 2, I don’t get the given answer.[/ul][/li] Even using a given example, stdDev and doing it ‘longhand’ both do not give the given answer. ---
**Author:** ![Jragon](https://avatars.discourse-cdn.com/v4/letter/j/e19b73/32.png) [@Jragon](https://boards.straightdope.com/u/Jragon)\ **Post date:** [April 20, 2014, 11:12pm UTC](https://boards.straightdope.com/t/stddev-on-ti-84/686557/6 "2014-04-20T23:12:42Z")
That handout is wrong (and incidentally, so was my answer, I used the population stddev, not the sample one). It’s squaring the wrong quantity. You don’t **square the sum**. you **sum the squares**. For 3 values, a,b, and c, and mean m, the sample stddev is: sqrt( ((a-m)^2 + (b-m)^2 + (c-m)^2)) / 2 ) ---
**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\ **Post date:** [April 20, 2014, 11:23pm UTC](https://boards.straightdope.com/t/stddev-on-ti-84/686557/7 "2014-04-20T23:23:47Z")
> [@Jragon](#): > > That handout is wrong (and incidentally, so was my answer, I used the population stddev, not the sample one). It’s squaring the wrong quantity. You don’t **square the sum**. you **sum the squares**. For 3 values, a,b, and c, and mean m, the sample stddev is: > > sqrt( ((a-m)^2 + (b-m)^2 + (c-m)^2)) / 2 ) OK, using that equation I get 0.0001366 – which is what the stdDev function gave me. So it looks like stdDev is standard deviation, and not relative standard deviation. ---
**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\ **Post date:** [April 20, 2014, 11:55pm UTC](https://boards.straightdope.com/t/stddev-on-ti-84/686557/8 "2014-04-20T23:55:17Z")
Too late to edit: The example says s = sqrt((2.56_10^-4 + 2.16_10^-4 + 0.020\*10^-4) g^2 / (3-1)) = 0.0154 g. As I said, I used the sum of the squares instead of the square of the sums to get the same answer I got by using the stdDev function on the calculator. The numbers given in the example are (x[sub]_i_[/sub] minus x-bar) squared. So in actuality, s = sqrt((2.56_10^-4 + 2.16_10^-4 + 0.020\*10^-4) g^2 / (3-1)) is right because the numbers are all squares. So where did the 0.0154 come from? I tried doing the manual calculation without squaring the sum of the squares, and came up with that.