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How to Calculate Standard Deviation

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.

  • view or download spreadsheet
    Standard deviation example spreadsheet in Google docs, click on file click on download and save the excel spreadsheet
deviation

Step 1

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

deviation

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.
deviation

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.
deviation

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.
deviation

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

deviation

© 2006 des donnelly

Comments

gepeTooRs on April 04, 2016:

I will surely visit back for more –Great job!

des donnelly (author) from NYC.... on April 10, 2014:

@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... :-)

Lindiwe Mazibuko on April 04, 2014:

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.

des donnelly (author) from NYC.... on March 26, 2013:

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

Pleapagenna on March 06, 2013:

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

des donnelly (author) from NYC.... on January 23, 2013:

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

Sweet on January 23, 2013:

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

des donnelly (author) from NYC.... on December 15, 2012:

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

dinesh-varyani on October 02, 2012:

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 .....

des donnelly (author) from NYC.... on September 21, 2012:

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

des donnelly (author) from NYC.... on September 21, 2012:

@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."

des donnelly (author) from NYC.... on September 21, 2012:

@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 :-)

Karina from Edinburgh on September 07, 2012:

Very informative and nicely explained. Well done!

Anastasia Phillis from Chicago on September 07, 2012:

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

FreezeFrame34 from Charleston SC on August 28, 2012:

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!

des donnelly (author) from NYC.... on August 19, 2012:

Thank you, I am glad!

pakistan on August 19, 2012:

Thanks very thanks sir

des donnelly (author) from NYC.... on August 18, 2012:

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

des donnelly (author) from NYC.... on August 18, 2012:

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

des donnelly (author) from NYC.... on August 18, 2012:

@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 !

Robbi on August 13, 2012:

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

Monica on August 12, 2012:

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!!! :-)

dravid on July 24, 2012:

thanks and nice post

Free2writ3 from Sharon Hill, Pennsylvania on July 24, 2012:

Very useful hub..Thanks alot.

whowas on July 23, 2012:

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.

des donnelly (author) from NYC.... on July 22, 2012:

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

hpgc on July 22, 2012:

absolutely brilliant!!

thanks for the hard work

saved me heaps of time =)

des donnelly (author) from NYC.... on July 16, 2012:

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

hello from kenya on July 15, 2012:

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

des donnelly (author) from NYC.... on June 28, 2012:

thank you Tahoor Khan :-)

tahoor khan on June 26, 2012:

very well done

des donnelly (author) from NYC.... on June 23, 2012:

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 !!

Kaila on June 20, 2012:

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

kaila on June 20, 2012:

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

des donnelly (author) from NYC.... on June 18, 2012:

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

des donnelly (author) from NYC.... on June 18, 2012:

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

des donnelly (author) from NYC.... on June 18, 2012:

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

jacob on June 14, 2012:

this helped me in my statistics exam

Robert Erich from California on June 14, 2012:

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!

Grace on June 07, 2012:

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

des donnelly (author) from NYC.... on May 29, 2012:

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

des donnelly (author) from NYC.... on May 29, 2012:

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

des donnelly (author) from NYC.... on May 29, 2012:

@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..

des donnelly (author) from NYC.... on May 29, 2012:

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

des donnelly (author) from NYC.... on May 29, 2012:

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

Shini on May 20, 2012:

Hi Drax, thanks for giving stepwise information about SD

Dr Pandula from Norway on May 10, 2012:

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

Eileen Goodall from Buckinghamshire, England on May 10, 2012:

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

kus kuas on May 08, 2012:

hi, thanks man, u helped me do my assignment

shalini on May 08, 2012:

Thanks soo much..timely help

des donnelly (author) from NYC.... on April 13, 2012:

Hi Marius.. greetings from Ireland :-)

des donnelly (author) from NYC.... on April 13, 2012:

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

Marius on April 03, 2012:

Greatings from Norway:-)

QuntileIndiangirl on March 26, 2012:

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

thanks

kimberly

des donnelly (author) from NYC.... on March 22, 2012:

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

priyanka on March 22, 2012:

thanks u make my efforts easy

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

des donnelly (author) from NYC.... on March 20, 2012:

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

des donnelly (author) from NYC.... on March 20, 2012:

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

lily lombardo on March 20, 2012:

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

louromano on March 20, 2012:

this is great, thanx for making it easy

des donnelly (author) from NYC.... on March 17, 2012:

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

Blake on March 17, 2012:

This is Awesome!!!!!

des donnelly (author) from NYC.... on March 10, 2012:

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

des donnelly (author) from NYC.... on March 10, 2012:

@ RG verry verry good lol :-)

Sara DK on March 08, 2012:

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

RG on March 04, 2012:

veryyyy veryyyy veryyy helpful. thanks :)

des donnelly (author) from NYC.... on February 12, 2012:

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

Mel on February 11, 2012:

Awesome example on standard deviation. Very helpful.

des donnelly (author) from NYC.... on February 08, 2012:

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 !!

S ANIL KUMAR on February 08, 2012:

I think it's better

Tom on February 03, 2012:

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

shunaynay on January 30, 2012:

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

Ragini Zatale on January 30, 2012:

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

amit on January 26, 2012:

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

lakee on January 23, 2012:

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

IB_MatheMacigian on January 17, 2012:

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. :)

Lal Nabi on January 15, 2012:

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

des donnelly (author) from NYC.... on January 15, 2012:

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

des donnelly (author) from NYC.... on January 15, 2012:

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

des donnelly (author) from NYC.... on January 15, 2012:

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

des donnelly (author) from NYC.... on January 15, 2012:

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

Lal Nabi on January 14, 2012:

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

Shiji on January 11, 2012:

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

pauline on January 05, 2012:

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.

Deen mohammad on January 03, 2012:

very usefull...easy to understand..thanks

des donnelly (author) from NYC.... on November 27, 2011:

@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

des donnelly (author) from NYC.... on November 27, 2011:

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

des donnelly (author) from NYC.... on November 27, 2011:

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

des donnelly (author) from NYC.... on November 27, 2011:

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

puzzled on November 26, 2011:

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

Swapnil on November 24, 2011:

Tnx...it was very helpful :)

PrimaD on November 17, 2011:

AWESOME!!!!!!!!

Ronald on November 16, 2011:

You saved my life dude!

des donnelly (author) from NYC.... on November 13, 2011:

Hi FruitySnoops... thanks for the comment !!

FruitySnoops on November 11, 2011:

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

des donnelly (author) from NYC.... on November 02, 2011:

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

Sheshe32 on November 02, 2011:

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

des donnelly (author) from NYC.... on October 29, 2011:

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

Sizz on October 29, 2011:

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

des donnelly (author) from NYC.... on October 25, 2011:

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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