# 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.

## 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 result is Standard Deviation

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SO STEP BY STEP;-

**1. get the Mean**

## 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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**6. square root of result is Standard Deviation**

## 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

.

- 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 1 - Photo 1

## 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

## Step 2a

Just hit enter

The Mean or Average will now appear in Cell 11

## Step 2a - Photo 2a

## Step 3

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 3 - Photo 3

## Step 4

The Standard Deviation will now appear in Cell 12

## Step 4 - Photo 4

## Pat yourself on the back if...

your final calc matches this...

## and the Final Score is...26.4

## Here is the link to the excel sheet, you can simply download it as an excel sheet and modify it to your needs.... :-)

- standard deviation_v1.xls - Google Docs

Standard deviation example spreadsheet in excel, just click on File and Download and save as excel spreadsheet

## 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....

## An Example of Using SD

## More Probability & Statistical Hubs by Drax

- What is Standard Deviation
- How to Use the Excel Descriptive Statistics tool

Use the Excel Descriptive Statistics tool to quickly calculate the Mean, Standard Error, Median, Mode, Standard Deviation, Sample Variance, Kurtosis, Skewness, Range, Minimum, Maximum, Sum, Count, Largest(1), Smallest(1), Confidence Level(95.0%)

## More by this Author

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a few robot poems from Irish poet Drax..

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## 225 comments

nicely done~

After i read your the page, i'm able to finish my statistic project..thankx dude

Love it, Drax.....the SD calculations, the Excel and the especially the poetry!! ;-)

awesome man!

very very informative, illustrated in a very simple way.

hi Drax, you should write a hub on how to get a hub score of 100. Wow!

I cheat and use my calculator to get a standard deviation. One thing I think that you could add to this hub (if you wanted to, but it is already a 100) is a bell curve graph to show the significance of standard deviation. If I remember correctly from school (a long time ago), x% of the data will fall within plus or minus 1 std dev, y% plus or minus 2 std dev, and I think its 99.7% will be within plus or minus three std dev. If you have enough data to calculate an accurate std dev, you can then determine the likely values of any new incoming data - would be good for a hub on how to make a living in Las Vegas...

Now about how you get that score of 100....

Drax, I see that this hub is now a 91. Interesting that the hub score fluxuates based on the number of incoming hits. I wonder what the standard deviation of the fluxuation on this hub is... :)

A word of advise, as a University academic, do not use wikipedia to get your answers as most of the time the information is just presented from people, and not from trustworthy sources.

thnx a lot for such a small and easy way of understanding the standard deviation.

Wow, exactlly what i needed help in THANK YOU i just got an A+ on my HW =D... your example is the simpliest out there on the web, and easyest 2 understand, thanks again!

Hey there,

THANKS for this!!! Loved the pic editorial, it was very helpful and easy to understand. I finally got it (at least I hope so) after many frustrating tries.

Thank you so much...

how to calculate the IRR?

cudn't ask for a better explanation. Thanks a million. Got an awful teacher who confused the entire topic (like everything else he teaches.) Got an exam tomorrow and jst conceptualised it. You may have just saved me from failing the exam. Thank you sincerely. Loved the poems as well.

Can you tell me why it's( Deviation) devided by n-1 but not by just n. What does it really mean?

Thank you for sharing the steps to calculate the standard deviation. You rock!

Thanks heaps for this example! It's by far the easiest to understand. I now understand Standard Deviations! lol.

Chrisssssssssssssss U'r Owsaaaam, U really help me xxxxxx

Thanks. Really helps in schoolwork.

cheers drax you're my hero.

Very well written hub .....

very much informative ......

Thank you very much for your great hub, for good advice, good wishes and support. Thanks for sharing your experience with all of us.

hi Drax..... i read a lot of sites about(Calculate Standard Deviation) but i cuod not understand...

now after i read your page understand 100%

great explanation

Excel explanation very great

its all Really helps

thanks a lot

( pls forgave me for my bad inglish)

hi Drax..... thanks for your reply

i wonder if you can help me in the following :

Linear Regression Indicator ...

calculation....

how To do linear regression indicator with excel

again and again thanks a lot

DUDE THE SQUARE ROOT IS NOT THE NUMBER MULTIPLIED BY ITS SELF

this is great, thanx for making it easy

Its really cool way of explaining! This is simple this is useful, you made complex definition to simple and understandable. Good Job.

It doesn't answer the question how to _calculate_. It just tels what the deviation is.

Excellent example for beginners thumb up**

thank you so much! explained so much better then my book and professor!

thanxxxx 4 such a nice help

Thanx

can anybody tel me the procedure to calculate standard deviation by a calculator...???

I can't believe I am looking at the standard deviation formula again. It has been ages but thank you for the reminder though.

Hi! Back to school grade 6! Thanks for helping us go back in time! -- Thanks

its really a gr8 work.. easy to understand..

Nice post!! Great work!!

Great info - Many Thanks for this site

omygosh! thanks so much! Deadline for my stats assignment is tmr and this practically save my life!! huge amount of thanks (: (: (:

thanks so so much, u really helpd me & now i understand

the topic is very informational and easy to understand. i believe it will be more useful for a beginner like me if you have time to illustrate also by example how to draw a bell curve for the given example data.thank you very much

good explaination

Thanks a ton i really learnt more from this dude thank u very very much

On an employee survey using an interval scale where 1 is low and 5 is high, which of the following results would show a distribution of responses with the most number of employees responding favorably, based on a response of 500 employees?

a) Mean = 4.0; standard deviation = .30

b) Mean = 4.2; standard deviation = .99

c) Mean = 4.5, standard deviation = .89

d) Mean = 3.9, standard deviation = .75

the answer is a.

How would you explain this?

this is simply great! :-) thnx lot Drax!

Thanks men... very very simply and clear. Any easier and my brain would have melted lol... Thanks. Lab report, DONE!

Thanks so much Drax! You really made it simple, I finally understand standard deviation!

thank uuuuuuuuuu

this helped alot! thanks

i was wondering if you could tell me how to work plus 1 S.D and minus 1 S.D

is it basically adding and subtracting the means from each number in the data??

your help is greatly appreciated

Such a very interesting information. We are currently studying how to get standard deviation, and it's somehow challenging due to different solving strategies.

Thanks for this. Very interesting. Nice post!

I use both excel and opencal (open office) and found that this is one good method for the deviation. Thanks for posting these pics, they were helpful.

Thank you! This helped me organize my chemistry work!

How do i find the standard deviation using likert scale

this didn't work why is it on the internet?

hey Drax,

After reading the posts made, it seems like u never answer back questions. Instead u just thank people for their compliment...

-I am Miss-understood about this

thanks a lot!

very helpful thankx

thanks a lot author....your explanation is very easy to understand....it is very much useful to me...

nice work. i understand it here more than what i have been thought

Hi

thank for your help

our proffesor teach our standard deviation and variance and error bar.

i neeed to know how i can using excel to plot the diagram

my data just 50 numbers

please help me

thanks a lot

Hi Drax,

Thank you so so much, u really helpd me & now i understand what is it Standard Deviation

COuld you help me forvanother question, please?

I don't understand what my instructor want for this homework

He would like me to 2. Use the Excel Descriptive Statistics tool (from the Analysis ToolPak) found in: File > Options > Add-Ins > Analysis ToolPak > Go > Analysis ToolPak (select) > OK. Then the Data Analysis tool will appear on the right of the Data ribbon.

And then question is

a. Obtain the descriptive statistics for Question #3: How many hours per day do you spend in total on Facebook, phone texting and e-mail? Format all non-integer values to two decimal places.

b. Are the data skewed? If so, in which direction and by how much?

He gave us a data but I don't know what he means and what I need to do

Could you help me,please?

Thank you very much

Thankyou it was good made me pass my homework mock exam as i copied and pasted it all :D x

Hi Drax,I for got to telll you that I used Excel 2003 version so I don't know it will make any different because my instructor used Excel 2007.

That's Analysis ToolPak also related to Creating a TRUE Excel Histogram for another home works.

I really appreaciate for you trying to help Drax because I would like to understand what I am doing but instructor did not explain

Thanks

This is awesome I searched like ten other sites then I found this one. It is definitely the best. Cheers Drax!

This really helped me out for my Algebra 1 honors (: Thanks lots!

thanks it really help me with my honors algbra homework

ii know how to do tis in school we do it 100 times a day i have it memerised did i mention i am 12?

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

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

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

You saved my life dude!

AWESOME!!!!!!!!

Tnx...it was very helpful :)

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

very usefull...easy to understand..thanks

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.

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

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

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

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. :)

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

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

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

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

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

I think it's better

Awesome example on standard deviation. Very helpful.

veryyyy veryyyy veryyy helpful. thanks :)

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

This is Awesome!!!!!

this is great, thanx for making it easy

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

thanks u make my efforts easy

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

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

thanks

kimberly

Greatings from Norway:-)

Thanks soo much..timely help

hi, thanks man, u helped me do my assignment

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

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

Hi Drax, thanks for giving stepwise information about SD

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

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 helped me in my statistics exam

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

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

very well done

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

absolutely brilliant!!

thanks for the hard work

saved me heaps of time =)

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.

Very useful hub..Thanks alot.

thanks and nice post

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

Thanks very thanks sir

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!

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

Very informative and nicely explained. Well done!

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 .....

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

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

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.

I will surely visit back for more –Great job!

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