How to Calculate Standard Deviation

Updated on March 6, 2019
Source

In this article, I will show you how to do the standard deviation, listing the 6 simple steps required, and showing the process manually and also describing how to do it using Excel (includes links to a downloadable spreadsheet of the examples given).

Six Straightforward Steps on How to Calculate Standard Deviation

  1. Get the mean
  2. Get the deviations
  3. Square these
  4. Add the squares
  5. Divide by total numbers less one
  6. Square root of the result is the standard deviation

Step-By-Step Example

Here is a step-by-step example of how to do the standard deviation with the manual method.

  1. Get the mean: To begin with, you need to find the mean or the average. For example, add 23, 92, 46, 55, 63, 94, 77, 38, 84, 26 = 598, then divide by 10 (the actual number of numbers) which is 598 divided by 10 = 59.8. So the mean or average of 23, 92, 46, 55, 63, 94, 77, 38, 84, 26 is 59.8
  2. Get the deviations: Subtract the mean from each of the numbers. The answers are: -36.8, 32.2, -13.8, -4.8, 3.2, 34.2, 17.2, -21.8, 24.2, -33.8
  3. Square These: To square means multiply them by themselves. The answers are: 1354.24, 1036.84, 190.44, 23.04, 10.24, 1169.64, 295.84, 475.24, 585.64, 1142.44
  4. Add the squares: The total of these numbers is 6,283.60
  5. Divide by total number of numbers less one: You had 10 numbers less 1 is 9 numbers, so 6283.60 divided by 9 = 698.18
  6. The Square root of the result is the standard deviation: A square root is the number multiplied by itself to get 698.18 which is 26.4, so 26.4 is the standard deviation.

Step-By-Step Example Using Excel

Now I will show you how to calculate the standard deviation using Excel. You will need to download the spreadsheet file below or make your own in order to do this.

Step 1

Enter your range of numbers as shown in cells 1 to 10.

Step 2

  • Place the cursor in Cell 11.
  • Go to the menu bar, select insert, select function: the insert function dialog box opens.
  • Click on the category and select Statistical.
  • In the window below select Average.
  • Hit enter.

Select the Insert Function
Select the Insert Function

Step 2a

  • When you hit enter another dialog box will appear asking you to confirm the range, i.e. the numbers in cells 1 to 10 that you wish to perform the calculation on.
  • Just hit enter.
  • The Mean or Average will now appear in Cell 11.

Step 3

  • Place the cursor in Cell 12.
  • Go to the menu bar, select insert, select function.
  • The function dialog box will open, select statistical, in the window below scroll down and select STDEV.

Step 4

  • When you hit enter another dialog box will appear asking you to confirm the range, i.e., the numbers in cells 1 to 10 that you wish to perform the calculation on. Since it automatically seeks to perform the calc on all the cells above you will have to change the range from D4:D14 to D4:D13.
  • The standard deviation will now appear in Cell 12.

Pat Yourself on the Back If

Your final calculation matches the image below.

and the Final Score is...26.4
and the Final Score is...26.4

What Does the Standard Deviation Tell You

The standard deviation is all about dispersion, how the set of numbers or data you have deviates from the mean; this is essentially a measure of uncertainty.

  • Low Deviation shows the numbers are all reasonably similar
  • High Deviation shows there is a lot of fluctuation in the numbers.

How can you use it:

  • Conducting investment research since this is an aid to measuring or calculating volatility.
  • Making weather comparison between locations or year to year.
  • Analysing agricultural yields and/or prices.
  • Almost everything to do with population analysis.
  • Lots of things in sports, with athletes, team performances, motorsports, horse racing, etc.

All these analyses help in prediction by looking closely at past performance.

Example: Using Deviation to Analyse Hub Scores

Just say we were using deviation to analyse hub scores, in the example below all the hub scores, are above 90, when the SD is calculated for this range the SD is 2.92. This is low; as a contrast the original calculation has hub scores from 23 to 94; in other words, there is a lot of volatility.

So if one wished to rank HubPages, it might be that those with a lower standard deviation, i.e., less volatility are more consistent, and so we enter the esoteric world of statistics. Imagine this was horses.

An Example of Using SD

Questions & Answers

    © 2006 des donnelly

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      • profile image

        gepeTooRs 

        3 years ago

        I will surely visit back for more –Great job!

      • Drax profile imageAUTHOR

        des donnelly 

        5 years ago from NYC....

        @Lindiwe Mazibuko.. thank you for taking the time to say so.. it is always lovely to receive feedback like this and I really hope that your exam went well... :-)

      • profile image

        Lindiwe Mazibuko 

        5 years ago

        Thank you very much for the information, i wanted these steps for the past two weeks and my tutor could not explain as clear as it is done on this site. Thanks again you have made my day and hope will done well on my exam.

      • Drax profile imageAUTHOR

        des donnelly 

        6 years ago from NYC....

        @Pleapagenna... life is full of resistance, this is a good thing :-)

      • profile image

        Pleapagenna 

        6 years ago

        We helpful to acquire on top of life however of late I've established a new level of resistance.

      • Drax profile imageAUTHOR

        des donnelly 

        6 years ago from NYC....

        that's.. Sweet... ;-)

      • profile image

        Sweet 

        6 years ago

        Thanks for this, I missed this in class, your explanation is probably a lot easier to understand anyways!

      • Drax profile imageAUTHOR

        des donnelly 

        6 years ago from NYC....

        @dinesh-varyani... thanks very much for the comment !

      • dinesh-varyani profile image

        dinesh-varyani 

        7 years ago

        Hi Drax,

        Its such a wonderful hub .... I am a Java Expert and write post regarding Java programs .... I am planning to write a Java program hub based on how to calculate standard deviation .... It will be dedicated to you ..... Thanks man .....

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @Pringoooals... again also apologies for the slow response, thanks very much for the comment.!

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @Anastasiaphillis... thanks for the comment, sorry for the slow response, poetry and mathematics actually go together very well, Einstein said;- "Pure mathematics is, in its way, the poetry of logical ideas."

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @FreezeFrame... sorry for the slow response, I seem to have missed a whole raft of comments here... I am very glad that you will be able to use this hub in education in any way at all... many thanks :-)

      • pringoooals profile image

        Karina 

        7 years ago from Edinburgh

        Very informative and nicely explained. Well done!

      • anastasiaphillis profile image

        Anastasia Phillis 

        7 years ago from Chicago

        I teach standard deviation once every 2 months, and the excel stuff was nice. Good idea to add some poetry :)

      • FreezeFrame34 profile image

        FreezeFrame34 

        7 years ago from Charleston SC

        Great and helpful! I took Algebra I and II, Geometry, Trig, and Honors Pre-Cal in high school as well as college classes, but never took Prob and Stats! This hub is easy to follow and I can use it to help my kids in the classroom!

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        Thank you, I am glad!

      • profile image

        pakistan 

        7 years ago

        Thanks very thanks sir

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @Monica and Robbi... I am glad that you found this explanation to be of benefit... thanks very much for the comments :-)

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @Sharon & Dravid... thanks very much for the comments

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @whowas.. thank you very much for the nice comment, it is great to receive encouragement and it is a great motivator to go and write articles that deliver some sort of usefulness to the reader. Thanks again !

      • profile image

        Robbi 

        7 years ago

        Thanks. This really helped me help my daughter with her maths homework.

      • profile image

        Monica 

        7 years ago

        Thank you so much for your simple breakdown on how to calculate a Standard Deviation both manually and using Excell. It was straight to the point and the example was quite helpful. I will now be able to help my sister understand the concept also.

        THANK YOU!!! :-)

      • profile image

        dravid 

        7 years ago

        thanks and nice post

      • Free2writ3 profile image

        Free2writ3 

        7 years ago from Sharon Hill, Pennsylvania

        Very useful hub..Thanks alot.

      • profile image

        whowas 

        7 years ago

        That is one of the clearest expositions of the methods of calculating standard deviation that I have ever seen. really, some tutors do seem to make these things unnecessarily complicated.

        Most mathematical and statistical procedures are only complex in their sum but each step is simple in itself. Your hub amply and ably demonstrates this principle.

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        HPGC... that's great !! this is exactly what Hubpages is about... people sharing stuff that saves time and adds value in some small way... :-)

      • profile image

        hpgc 

        7 years ago

        absolutely brilliant!!

        thanks for the hard work

        saved me heaps of time =)

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        Hello .. hello from kenya :-) this is excellent and I am delighted to know this helped in some small way... thanks Drax

      • profile image

        hello from kenya 

        7 years ago

        fantastic those steps has enabled me to understand how to calculate standard deviation.

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        thank you Tahoor Khan :-)

      • profile image

        tahoor khan 

        7 years ago

        very well done

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        Hi Kaila.. thanks for the comment :-) there is a difference in the formula for calculating Standard Deviation if the set of numbers you have is the entire Population or a Sample of the entire Population -

        for the Population it is N

        for the Sample it is N-1

        ..if you would like to post your numbers I will take them and make examples to show what happens with the formula !!

      • profile image

        Kaila 

        7 years ago

        this is a really hlpful page and its very much appreciated that you take the time to explain how to figure out standard deviation, although i have to say that when you say you divide the total number less one. i find that my answers are never correct. they are only correct when i divide by the total numbers. the equations in my foundation math book also say that it is divide by total numbers. it says nothing about divide less one. other than that this page helps keep me on track until i have it memorized. so thank you

      • profile image

        kaila 

        7 years ago

        this is very helpful for me, except it doesn't work when you divide by the number less one.... you need to divide by the number to get the correct answer

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @Jacob... that's good since this is the whole idea, to be able to convey what it is about... thanks for the comment :-)

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @ Robert Erich... yes it is nice to be at the top of any Google search :-) thanks !!

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @Grace... thanks for the comment and for the nice words.. :-)

      • profile image

        jacob 

        7 years ago

        this helped me in my statistics exam

      • Robert Erich profile image

        Robert Erich 

        7 years ago from California

        Very helpful information! Thanks for writing. I Googled help to find this and found a fellow hubber as the top result! Great to know that we can make it up there. Look forward to stumbling upon you again!

      • profile image

        Grace 

        7 years ago

        This is by far the most helpful and strait forward explanation I have ever seen. THANKS!

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @Shini.. thanks a lot for taking the time to comment :-)

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @pandula.. thanks very much for the vote up !!

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @Eileen Goodall.. thanks Eileen, I feel the same about algebra, it is always frustrating if the fundamental is not explained clearly to you in school..

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @kus kuas... thanks for the comment !!

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @shalini... glad it was right place right time.. :-)

      • profile image

        Shini 

        7 years ago

        Hi Drax, thanks for giving stepwise information about SD

      • pandula77 profile image

        Dr Pandula 

        7 years ago from Norway

        Hey Drax, thanks for the info. A complex topic made easy. voted up!

      • Eileen Goodall profile image

        Eileen Goodall 

        7 years ago from Buckinghamshire, England

        I remember everyone struggling with this when I did my Psychology stats - great posting!

      • profile image

        kus kuas 

        7 years ago

        hi, thanks man, u helped me do my assignment

      • profile image

        shalini 

        7 years ago

        Thanks soo much..timely help

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        Hi Marius.. greetings from Ireland :-)

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        Hi Kimberly... thanks for taking the time to post a comment and I am glad it was of help.. :-)

      • profile image

        Marius 

        7 years ago

        Greatings from Norway:-)

      • profile image

        QuntileIndiangirl 

        7 years ago

        thnks drax i really needed this for hw i did this before but didn't understand now i do.

        thanks

        kimberly

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @ priyanka.. that is excellent since that was the objective to make it able to be understood... thanks for the comment ... :-)

      • profile image

        priyanka 

        7 years ago

        thanks u make my efforts easy

        the description is so simple....thank u so much

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @lily lombardo... thank You.. for the comment :-)

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @louromano great that you found it to be of some help... thanks for the comment :-)

      • profile image

        lily lombardo 

        7 years ago

        thanks for all the help. It helped me a TON!

      • louromano profile image

        louromano 

        7 years ago

        this is great, thanx for making it easy

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        Hey Blake... thanks for the comment :-)

      • profile image

        Blake 

        7 years ago

        This is Awesome!!!!!

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @Sara... thanks, glad to be of assistance...

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @ RG verry verry good lol :-)

      • profile image

        Sara DK 

        7 years ago

        Thanks a lot :) Very helpful step by step for my research assignment!

      • profile image

        RG 

        7 years ago

        veryyyy veryyyy veryyy helpful. thanks :)

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        Hi Mel... thanks very much for the comment :-)

      • profile image

        Mel 

        7 years ago

        Awesome example on standard deviation. Very helpful.

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        Hi folks... thanks for much for all the comment, I see a number of questions contained in these last comments and I will definitely try to make additional hubs addressing these aspects... Thanks to All !!

      • profile image

        S ANIL KUMAR 

        7 years ago

        I think it's better

      • profile image

        Tom 

        7 years ago

        Thats was fantastic. I think this is all I needed and really helped moi. Thanks man!!

      • profile image

        shunaynay 

        7 years ago

        thanks:) helped me alot for my hmwk!!!!

      • profile image

        Ragini Zatale 

        7 years ago

        Thnks alot .......it was so useful to me...

      • profile image

        amit 

        7 years ago

        hey how to calculate the standard error of xy plot????

      • profile image

        lakee 

        7 years ago

        You made it really simple for me buddy!! Thanks!

      • profile image

        IB_MatheMacigian 

        7 years ago

        Great, simple quidance, but isn't this the formula for the unbiased estimate of the population variance, rather than the standard deviation which only consideres the sample given?

        Difference between these two would be in step 5, for standard deviation one does not need to substract 1 from the divisor. :)

      • profile image

        Lal Nabi 

        7 years ago

        why we use standard deviation means what is the application of standard deviation..

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @Lal Nabi... I am very glad that it can help convey what deviation is all about, thanks for the comment !!

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @Shiji... thanks very much for the comment, it is appreciated !!

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @Pauline.. thanks for the comment, deviation is a tricky subject and it is always important to learn the fundamental, then you never forgot :-)

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @Deen Mohammad... thanks very much, it is good to know this always !

      • profile image

        Lal Nabi 

        7 years ago

        very good way to learn something. easy way for understanding.

      • profile image

        Shiji 

        7 years ago

        Such a wonderful presentation!!!!!!!!!!!!!!! Thanks dude

      • profile image

        pauline 

        7 years ago

        hi, i am really learning and i am enjoying your piece of work i hope i understand these better. since it is simplified for those who are slow learners!!!!!!!!! thanks a lot.

      • profile image

        Deen mohammad 

        7 years ago

        very usefull...easy to understand..thanks

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @Pazzled... missing data usually cannot be found, you have to guess... it depends on what % of data is missing, if say 30% of the results are missing or just 1%.

        Depending on the data size here are 4 choices;-

        1. the questions/cases are deleted with the missing data, if it is small percent of overall study, answers, number range

        2. You use Single Imputation which means you use other methods to help you guess the missing values, the real simple way is to use the mean or median

        3. Next you can use complicated things like stochastic regression or EM Imputation to help predict.

        4. Multiple Imputation really means using more complicated tools to predict but now your whole data is becoming more unreliable.

        If you are not missing lots of data you could simply use the mean or the median and then you could make a little table of the deviation using both sets of data to show you know it makes a difference, your table could have SD with these three sets of figures...

        1. with the missing data

        2. just substituting the missing with the mean

        3. just substituting the missing with the median

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        Hi Swapnil... good of you to say so... thanks !!

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        Hey PrimaD... good is awesome is good... thanks a lot :-)

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        @Ronald... good man Ronald, thanks... keeping the old life statistics current is a good habit... !!

      • profile image

        puzzled 

        7 years ago

        What if you have a missing data, how do you find it if you have a standard deviation of 3?

      • profile image

        Swapnil 

        7 years ago

        Tnx...it was very helpful :)

      • profile image

        PrimaD 

        7 years ago

        AWESOME!!!!!!!!

      • profile image

        Ronald 

        7 years ago

        You saved my life dude!

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        Hi FruitySnoops... thanks for the comment !!

      • profile image

        FruitySnoops 

        7 years ago

        Thanx a lot!!! very very awesome. keep it up

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        Hey thanks Sheshe... I feel that a lot when I cannot understand WTF they are trying to tell me....

      • profile image

        Sheshe32 

        7 years ago

        i absolutely love this after 20 yrs out of school i was unable to have this make sense wow thank you so much!! :)0

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        Sizz... thank you for saying so, it is appreciated :-)

      • profile image

        Sizz 

        7 years ago

        really well and clearly explained, thank you so much! brilliant help to me this was!

      • Drax profile imageAUTHOR

        des donnelly 

        7 years ago from NYC....

        Well Sara... that is fantastic, it is great to have the talent to be able to memorise mathematical things... it's good for the brain .. like running :-)

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