# Standard Deviation – Why do we square the values

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This topic contains 32 replies, has 10 voices, and was last updated by Mike Carnell 11 months, 1 week ago.

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- September 14, 2010 at 1:06 pm #53574

wilsParticipant@michsigma**Include @michsigma in your post and this person will**

be notified via email.Ok…no beating me up on this question…just a curiosity that I can’t find the answer to.

So, in the method for calculating the standard deviation at one point we subtract the mean from a data point and we do that with all the data points. Next we square the results of each subtraction, which effectively eliminates the negative signs.

So, the question is…why do we square? Why not just take the absolute value.

Thanks!

0September 15, 2010 at 11:08 am #190743

MBBinWIParticipant@MBBinWI**Include @MBBinWI in your post and this person will**

be notified via email.**michsigma wrote:**Ok…no beating me up on this question…just a curiosity that I can’t find the answer to.

So, in the method for calculating the standard deviation at one point we subtract the mean from a data point and we do that with all the data points. Next we square the results of each subtraction, which effectively eliminates the negative signs.

So, the question is…why do we square? Why not just take the absolute value.

Thanks!

OK, all together now – Variations are additive, std dev’s are not.

It’s just how the math works. Kind of like asking why a right triangle is a^2 + b^2 = c^2, it just is.

0September 15, 2010 at 11:58 am #190744Mich,

Let’s add the difference as you said, what will you get

**Zero**.

Why Zero ?

Because we are subtracting from Mean.Which will not give you any measure i.e. how much the data vary each side from mean.

To overcome this, it makes sense to first square it and then take square-root.

If statisticians had chosen to subtract Min. value from data points and then calculate deviation then there was no need to square it.

So it is because , how we define it. e.g. Left is -ve, Right is +ve etc.

Other option could have been to take modulus and then sum it then it would be a different measure.

Anupam

0September 15, 2010 at 3:56 pm #190745

Robert ButlerParticipant@rbutler**Include @rbutler in your post and this person will**

be notified via email.You could run an analysis using the absolute deviations instead of the measure that is used. I was trying to find the original referernce so I could give you all of the gory details but, at the moment, I can’t seem to locate the book I want. By way of an anemic substitute I’ll offer the following from pp.29 Statistical Methods 7th Edition Snedecor and Cochran:

“The average of the absolute deviations could be used [to measure the amount of variation] but for several reasons a different measure was adopted around 1800 – the population standard deviation.”

0September 17, 2010 at 4:41 pm #190754

PaulonisParticipant@paulonis**Include @paulonis in your post and this person will**

be notified via email.There was some influential work that concluded that the sample standard deviation was a more efficient estimator of the population statistic than the sample mean deviation was of it’s population statistic. There is a great deal of debate regarding under which assumptions this is true. Nevertheless, standard deviation caught on and became the generally accepted statistic.

More importantly in my mind, the square operation is much nicer mathematically than the absolute value operation. The absolute value makes analytical calculations much more difficult when using the mean deviation.

A nice reference is:

http://www.leeds.ac.uk/educol/documents/00003759.htm

0September 20, 2010 at 2:06 pm #190768

wilsParticipant@michsigma**Include @michsigma in your post and this person will**

be notified via email.Thanks everyone….especially Mr. Butler and Paulonis for the refernces….I knew the truth was out there!

0May 2, 2015 at 9:16 pm #198222

vishalThe other reasoning may be:-

Mean is the central point of the data points and the difference on -ve and +ve side can be expressed as mean, if we end up taking absolute value the we will be gaving sd “2” as a result every time

2*mean/mean

0May 3, 2015 at 5:09 am #198223

Amit Kumar OjhaParticipant@AmitOjha**Include @AmitOjha in your post and this person will**

be notified via email.The main difference between Mean Absolute Deviation (calculated by taking the absolute value of difference around mean) and standard deviation (calculated by squaring the differences and then adding them up and finally taking the Square Root) is that

**Standard Deviation gives more weightage to the extreme value and hence is considered a better estimation than Mean Absolute Deviation.**0May 4, 2015 at 6:10 am #198227

Chris SeiderParticipant@cseider**Include @cseider in your post and this person will**

be notified via email.You can add squares and do proper statistics such as ANOVA, etc. using sums of squares.

0February 26, 2017 at 8:23 pm #200688

KevinHi Wils,

I think the answer is in the DNS of this website. We love saying “Six Sigma”! lol

Best,

Kevin0February 27, 2017 at 6:36 am #200709

MBBinWIParticipant@MBBinWI**Include @MBBinWI in your post and this person will**

be notified via email.Wow, six and a half years later, Kevin comes through with a witty answer. Wils is long gone, and you’re answer wasn’t particularly witty.

0February 27, 2017 at 6:40 am #200712

Mike CarnellParticipant@Mike-Carnell**Include @Mike-Carnell in your post and this person will**

be notified via email.That is a lot of answers for a really simple question.

0February 27, 2017 at 7:51 am #200719

Andrew ParrParticipant@Andy-Parr**Include @Andy-Parr in your post and this person will**

be notified via email.@MBBinWI maybe it just proves that even though Kevin is older now it still isn’t wise to leave him Home Alone.

0February 28, 2017 at 8:33 am #200745

MBBinWIParticipant@MBBinWI**Include @MBBinWI in your post and this person will**

be notified via email.@Robert-Butler – are you trying to assume the persona of a well respected forum member?

@Katie-barry – I think we have an imposter here.

0February 28, 2017 at 8:35 am #200746

MBBinWIParticipant@MBBinWI**Include @MBBinWI in your post and this person will**

be notified via email.@katiebarry – sorry, messed up your handle. Looks like we have an imposter trying to assume the identity of our friend @rbutler

0February 28, 2017 at 8:39 am #200748

Robert ButlerParticipant@rbutler**Include @rbutler in your post and this person will**

be notified via email.@MBBinWI – no, we don’t. When the forum shifted over to ID’s with the @ sign attached I assumed the new ID had to be all one word so I chose rbutler. There is a problem with this because if you try to search my older posts you have to use the full name – the 2010 post above was made before the @ switch and it looks like the @ was just appended to my name in the posts before the change.

0February 28, 2017 at 8:45 am #200749

Robert ButlerParticipant@rbutler**Include @rbutler in your post and this person will**

be notified via email.P.S. it would be nice if the site could change all of my post ID’s to one or the other but I suspect that would be more trouble than it is worth.

0February 28, 2017 at 9:05 am #200752

Mike CarnellParticipant@Mike-Carnell**Include @Mike-Carnell in your post and this person will**

be notified via email.@rbutler I still keep up with your posts. I love your answers. Very straight forward responses to seemingly complex questions.

What would be great would be to have someone pull together all your responses into a book. That was done with some totally inane blogs years ago for another person. On a scale of 1-10 in terms of helpful it was about a -100. At least yours would provide some useful information.

Take care.

@KatieBerry you are tough. You have to have over 10 years refereeing these food fights.

0February 28, 2017 at 9:40 am #200755

Katie Barry@KatieBarry**Include @KatieBarry in your post and this person will**

be notified via email.@mike-carnell I’m definitely tough!! Hard as nails. Unless you see me watching a sappy commercial when I *might* cry. :)

0February 28, 2017 at 11:19 am #200757

Andy-Parr@Andy-Parr**Include @Andy-Parr in your post and this person will**

be notified via email.@katiebarry you make whether to cry or not seem like a choice. If so you are definitely as hard as nails or maybe just a smiling assassin.

0February 28, 2017 at 1:04 pm #200758

Mike CarnellParticipant@Mike-Carnell**Include @Mike-Carnell in your post and this person will**

be notified via email.@katiebarry Consuelo watches that stuff too. Hallmark and WE channel. I think there are others with that same romance novel programing. If I have to sit through Pride and Prejudice one more time……

0February 28, 2017 at 1:36 pm #200761

Robert ButlerParticipant@rbutler**Include @rbutler in your post and this person will**

be notified via email.@mike-carnell you said “If I have to sit through Pride and Prejudice one more time……”…then, of course, you, like me, will do it! :-) Question: does Consuelo own just one version or does she have all the different performances of PandP?

0February 28, 2017 at 1:42 pm #200762

Mike CarnellParticipant@Mike-Carnell**Include @Mike-Carnell in your post and this person will**

be notified via email.@rbutler I will do it just like you said but if you put on John Wick as soon as it is over they recognize cause and effect pretty quickly. That whole puppy thing is tougher on them than the entire rest of the movie.

Near as I can tell there is just one version in the house but I don’t watch close enough to tell. I did draw the line at P&P with Zombies. I am not doing that one ever again.

0February 28, 2017 at 1:51 pm #200763

Katie BarryKeymaster@KatieBarry**Include @KatieBarry in your post and this person will**

be notified via email.@andy-parr I am TOTALLY going with smiling assassin from now on! Love it.

0February 28, 2017 at 1:52 pm #200764

Katie BarryKeymaster@KatieBarry**Include @KatieBarry in your post and this person will**

be notified via email.@mike-carnell and @rbutler Consuelo is right. You can’t watch P&P enough times. My preference is the BBC version with Colin Firth. The newer movie with Keira Knightley is good, too, but I’m loyal to the earlier version.

I heard there’s a new dog in John Wick 2. (Spoiler alert) I don’t think I’ve ever recovered from the puppy dying in the first one.

0February 28, 2017 at 2:01 pm #200765

Mike CarnellParticipant@Mike-Carnell**Include @Mike-Carnell in your post and this person will**

be notified via email.@katiebarry I have seen the Keira Knightly version. That woman is way to skinny. You do stories from back then you need curves.

There is a new dog in JW2. That whole thing “You make me watch P&P again then we are doing JW.” Life is a negotiation.

0February 28, 2017 at 5:04 pm #200766

MBBinWIParticipant@MBBinWI**Include @MBBinWI in your post and this person will**

be notified via email.@katiebarry – nevermind

@rbutler – the thing that caused my suspicions was that Robert-butler didn’t have any points. Glad to know you’re not being spoofed.

@mike-carnell – you’ve given me a new movie to search out – and not PandP ;-}

0February 28, 2017 at 5:27 pm #200777

Katie Barry@KatieBarry**Include @KatieBarry in your post and this person will**

be notified via email.@mike-carnell Fully agree re Keira casting. She’s a great actress, but was not a good physical representative of Elizabeth.

Adding JW2 to my list of movies to see. It’s quite long, but I’ll get there eventually.

0February 28, 2017 at 5:38 pm #200781

Katie BarryKeymaster@KatieBarry**Include @KatieBarry in your post and this person will**

be notified via email.@rbutler said:

P.S. it would be nice if the site could change all of my post ID’s to one or the other but I suspect that would be more trouble than it is worth.

— Done! :)

0February 28, 2017 at 5:53 pm #200788

MBBinWIParticipant@MBBinWI**Include @MBBinWI in your post and this person will**

be notified via email.@katiebarry – of course, ’cause you’re the forum goddess. ;-}

0February 28, 2017 at 7:43 pm #200789

Robert ButlerParticipant@rbutler**Include @rbutler in your post and this person will**

be notified via email.Thanks Katie – much appreciated. Interestingly enough (I just got home from a very very long work day) when I checked my home e-mail a minute or so ago MBBinWI’s query to the @robert Butler name showed up in my home e-mail.

Oh yes, PandP for Katie and Consuelo – My wife’s collection

1. BBC Video – PandP starring Elizabeth Garvie and David Rintoul

2. A&E PandP The Special Edition (2 discs) Starring Colin Firth and Jennifer Ehle

3. Focus Features PandP Starring Keira Knightley and Matthew MacfadyenShe likes all of them equally – zero variation.

0June 17, 2018 at 7:58 am #202681

Carlos tarnowskiIf you take the mean of the absolute deviation you will have exactly what you did, which is the mean of the absolute deviations for your sample. But the inferences you could make about your population gets limited, because You can’t use the properties from the distribution curve it comes from, as it uses sd as an input parameter. So I think, first they tried to work out what parameters were related to the distribution population curve and sd was always there, and the absolute mean value no, then, sd is used for that purpose, not eliminating the information the absolute deviation gives, too.

But it is just an intuitive opinion, not based on any book.

0June 18, 2018 at 8:11 am #202683

Mike CarnellParticipant@Mike-Carnell**Include @Mike-Carnell in your post and this person will**

be notified via email.Carlos You are responding to a question from over 7 years ago. The last post from Robert Butler was 16 months ago and we had all deviated from the original questions.

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