# How to Calculate Standard Deviation

How to do standard deviation, listing the 6 simple steps required, showing the process manually and also describing how to do it using Excel - includes links to a downloadable spreadsheet of the examples given.

## 6. Square root of result is Standard Deviation

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SO STEP BY STEP;-

## to begin you need the mean or the average, for example add 23, 92, 46, 55, 63, 94, 77, 38, 84, 26 ... = 598 divide by 10 (the actual number of numbers) 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

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## 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

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## 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

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## 4. add the squares

total of these numbers is 6,283.60

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## 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

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## square root is the number multiplied by itself to get 698.18 which is:-

26.4 so 26.4 is the Standard Deviation...

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Ok so above is the manual method of doing this

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## Step by step example using Excel...

Calculating standard deviation using Excel

.

## 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 2 - Photo 2

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

same as before 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 perfrom 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 calc matches this...

## What Does Standard Deviation Tell You

Standard deviation is all about dispersion - how the set of numbers or data you have deviate 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, teams performances, motorsport, horse racing

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 calc has hub scores from 23 to 94 in other words there is a lot of volatility...

So if one wished to rank hubpages it may 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....

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• gepeTooRs 17 months ago

I will surely visit back for more –Great job!

• Author

des donnelly 3 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... :-)

• Lindiwe Mazibuko 3 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.

• Author

des donnelly 4 years ago from NYC....

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

• Pleapagenna 4 years ago

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

• Author

des donnelly 4 years ago from NYC....

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

• Sweet 4 years ago

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

• Author

des donnelly 4 years ago from NYC....

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

• dinesh-varyani 4 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 .....

• Author

des donnelly 5 years ago from NYC....

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

• Author

des donnelly 5 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."

• Author

des donnelly 5 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 :-)

• Karina 5 years ago from Edinburgh

Very informative and nicely explained. Well done!

• Anastasia Phillis 5 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 5 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!

• Author

des donnelly 5 years ago from NYC....

Thank you, I am glad!

• pakistan 5 years ago

Thanks very thanks sir

• Author

des donnelly 5 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 :-)

• Author

des donnelly 5 years ago from NYC....

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

• Author

des donnelly 5 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 !

• Robbi 5 years ago

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

• Monica 5 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!!! :-)

• dravid 5 years ago

thanks and nice post

• Free2writ3 5 years ago from Sharon Hill, Pennsylvania

Very useful hub..Thanks alot.

• whowas 5 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.

• Author

des donnelly 5 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... :-)

• hpgc 5 years ago

absolutely brilliant!!

thanks for the hard work

saved me heaps of time =)

• Author

des donnelly 5 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

• hello from kenya 5 years ago

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

• Author

des donnelly 5 years ago from NYC....

thank you Tahoor Khan :-)

• tahoor khan 5 years ago

very well done

• Author

des donnelly 5 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 !!

• Kaila 5 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

• kaila 5 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

• Author

des donnelly 5 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 :-)

• Author

des donnelly 5 years ago from NYC....

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

• Author

des donnelly 5 years ago from NYC....

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

• jacob 5 years ago

this helped me in my statistics exam

• Robert Erich 5 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!

• Grace 5 years ago

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

• Author

des donnelly 5 years ago from NYC....

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

• Author

des donnelly 5 years ago from NYC....

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

• Author

des donnelly 5 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..

• Author

des donnelly 5 years ago from NYC....

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

• Author

des donnelly 5 years ago from NYC....

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

• Shini 5 years ago

Hi Drax, thanks for giving stepwise information about SD

• pandula77 5 years ago from Norway

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

• Eileen Goodall 5 years ago from Buckinghamshire, England

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

• kus kuas 5 years ago

hi, thanks man, u helped me do my assignment

• shalini 5 years ago

Thanks soo much..timely help

• Author

des donnelly 5 years ago from NYC....

Hi Marius.. greetings from Ireland :-)

• Author

des donnelly 5 years ago from NYC....

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

• Marius 5 years ago

Greatings from Norway:-)

• QuntileIndiangirl 5 years ago

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

thanks

kimberly

• Author

des donnelly 5 years ago from NYC....

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

• priyanka 5 years ago

thanks u make my efforts easy

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

• Author

des donnelly 5 years ago from NYC....

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

• Author

des donnelly 5 years ago from NYC....

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

• lily lombardo 5 years ago

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

• louromano 5 years ago

this is great, thanx for making it easy

• Author

des donnelly 5 years ago from NYC....

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

• Blake 5 years ago

This is Awesome!!!!!

• Author

des donnelly 5 years ago from NYC....

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

• Author

des donnelly 5 years ago from NYC....

@ RG verry verry good lol :-)

• Sara DK 5 years ago

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

• RG 5 years ago

veryyyy veryyyy veryyy helpful. thanks :)

• Author

des donnelly 5 years ago from NYC....

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

• Mel 5 years ago

Awesome example on standard deviation. Very helpful.

• Author

des donnelly 5 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 !!

• S ANIL KUMAR 5 years ago

I think it's better

• Tom 5 years ago

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

• shunaynay 5 years ago

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

• Ragini Zatale 5 years ago

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

• amit 5 years ago

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

• lakee 5 years ago

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

• IB_MatheMacigian 5 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. :)

• Lal Nabi 5 years ago

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

• Author

des donnelly 5 years ago from NYC....

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

• Author

des donnelly 5 years ago from NYC....

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

• Author

des donnelly 5 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 :-)

• Author

des donnelly 5 years ago from NYC....

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

• Lal Nabi 5 years ago

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

• Shiji 5 years ago

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

• pauline 5 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.

• Deen mohammad 5 years ago

very usefull...easy to understand..thanks

• Author

des donnelly 5 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

• Author

des donnelly 5 years ago from NYC....

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

• Author

des donnelly 5 years ago from NYC....

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

• Author

des donnelly 5 years ago from NYC....

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

• puzzled 5 years ago

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

• Swapnil 5 years ago

Tnx...it was very helpful :)

• PrimaD 5 years ago

AWESOME!!!!!!!!

• Ronald 5 years ago

You saved my life dude!

• Author

des donnelly 5 years ago from NYC....

Hi FruitySnoops... thanks for the comment !!

• FruitySnoops 5 years ago

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

• Author

des donnelly 5 years ago from NYC....

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

• Sheshe32 5 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

• Author

des donnelly 5 years ago from NYC....

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

• Sizz 5 years ago

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

• Author

des donnelly 5 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 :-)