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
- Get the mean
- Get the deviations
- Square these
- Add the squares
- Divide by total numbers less one
- 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.
- 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
- 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
- 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
- Add the squares: The total of these numbers is 6,283.60
- 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
- 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
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.
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.
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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Comments
I will surely visit back for more –Great job!
- AUTHOR
@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... :-)
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.
- AUTHOR
@Pleapagenna... life is full of resistance, this is a good thing :-)
We helpful to acquire on top of life however of late I've established a new level of resistance.
- AUTHOR
that's.. Sweet... ;-)
Thanks for this, I missed this in class, your explanation is probably a lot easier to understand anyways!
- AUTHOR
@dinesh-varyani... thanks very much for the comment !
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 .....
- AUTHOR
@Pringoooals... again also apologies for the slow response, thanks very much for the comment.!
- AUTHOR
@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."
- AUTHOR
@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 :-)
Very informative and nicely explained. Well done!
I teach standard deviation once every 2 months, and the excel stuff was nice. Good idea to add some poetry :)
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!
- AUTHOR
Thank you, I am glad!
Thanks very thanks sir
- AUTHOR
@Monica and Robbi... I am glad that you found this explanation to be of benefit... thanks very much for the comments :-)
- AUTHOR
@Sharon & Dravid... thanks very much for the comments
- AUTHOR
@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 !
Thanks. This really helped me help my daughter with her maths homework.
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!!! :-)
thanks and nice post
Very useful hub..Thanks alot.
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.
- AUTHOR
HPGC... that's great !! this is exactly what Hubpages is about... people sharing stuff that saves time and adds value in some small way... :-)
absolutely brilliant!!
thanks for the hard work
saved me heaps of time =)
- AUTHOR
Hello .. hello from kenya :-) this is excellent and I am delighted to know this helped in some small way... thanks Drax
fantastic those steps has enabled me to understand how to calculate standard deviation.
- AUTHOR
thank you Tahoor Khan :-)
very well done
- AUTHOR
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 !!
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
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
- AUTHOR
@Jacob... that's good since this is the whole idea, to be able to convey what it is about... thanks for the comment :-)
- AUTHOR
@ Robert Erich... yes it is nice to be at the top of any Google search :-) thanks !!
- AUTHOR
@Grace... thanks for the comment and for the nice words.. :-)
this helped me in my statistics exam
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!
This is by far the most helpful and strait forward explanation I have ever seen. THANKS!
- AUTHOR
@Shini.. thanks a lot for taking the time to comment :-)
- AUTHOR
@pandula.. thanks very much for the vote up !!
- AUTHOR
@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..
- AUTHOR
@kus kuas... thanks for the comment !!
- AUTHOR
@shalini... glad it was right place right time.. :-)
Hi Drax, thanks for giving stepwise information about SD
Hey Drax, thanks for the info. A complex topic made easy. voted up!
I remember everyone struggling with this when I did my Psychology stats - great posting!
hi, thanks man, u helped me do my assignment
Thanks soo much..timely help
- AUTHOR
Hi Marius.. greetings from Ireland :-)
- AUTHOR
Hi Kimberly... thanks for taking the time to post a comment and I am glad it was of help.. :-)
Greatings from Norway:-)
thnks drax i really needed this for hw i did this before but didn't understand now i do.
thanks
kimberly
- AUTHOR
@ priyanka.. that is excellent since that was the objective to make it able to be understood... thanks for the comment ... :-)
thanks u make my efforts easy
the description is so simple....thank u so much
- AUTHOR
@lily lombardo... thank You.. for the comment :-)
- AUTHOR
@louromano great that you found it to be of some help... thanks for the comment :-)
thanks for all the help. It helped me a TON!
this is great, thanx for making it easy
- AUTHOR
Hey Blake... thanks for the comment :-)
This is Awesome!!!!!
- AUTHOR
@Sara... thanks, glad to be of assistance...
- AUTHOR
@ RG verry verry good lol :-)
Thanks a lot :) Very helpful step by step for my research assignment!
veryyyy veryyyy veryyy helpful. thanks :)
- AUTHOR
Hi Mel... thanks very much for the comment :-)
Awesome example on standard deviation. Very helpful.
- AUTHOR
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 !!
I think it's better
Thats was fantastic. I think this is all I needed and really helped moi. Thanks man!!
thanks:) helped me alot for my hmwk!!!!
Thnks alot .......it was so useful to me...
hey how to calculate the standard error of xy plot????
You made it really simple for me buddy!! Thanks!
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. :)
why we use standard deviation means what is the application of standard deviation..
- AUTHOR
@Lal Nabi... I am very glad that it can help convey what deviation is all about, thanks for the comment !!
- AUTHOR
@Shiji... thanks very much for the comment, it is appreciated !!
- AUTHOR
@Pauline.. thanks for the comment, deviation is a tricky subject and it is always important to learn the fundamental, then you never forgot :-)
- AUTHOR
@Deen Mohammad... thanks very much, it is good to know this always !
very good way to learn something. easy way for understanding.
Such a wonderful presentation!!!!!!!!!!!!!!! Thanks dude
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.
very usefull...easy to understand..thanks
- AUTHOR
@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
- AUTHOR
Hi Swapnil... good of you to say so... thanks !!
- AUTHOR
Hey PrimaD... good is awesome is good... thanks a lot :-)
- AUTHOR
@Ronald... good man Ronald, thanks... keeping the old life statistics current is a good habit... !!
What if you have a missing data, how do you find it if you have a standard deviation of 3?
Tnx...it was very helpful :)
AWESOME!!!!!!!!
You saved my life dude!
- AUTHOR
Hi FruitySnoops... thanks for the comment !!
Thanx a lot!!! very very awesome. keep it up
- AUTHOR
Hey thanks Sheshe... I feel that a lot when I cannot understand WTF they are trying to tell me....
i absolutely love this after 20 yrs out of school i was unable to have this make sense wow thank you so much!! :)0
- AUTHOR
Sizz... thank you for saying so, it is appreciated :-)
really well and clearly explained, thank you so much! brilliant help to me this was!
- AUTHOR
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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