How to Calculate Standard Deviation
96So six straightforward steps 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
------------------------------------------------------
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
____________________________________________________
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
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. 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...
_____________________________________________________
Ok so above is the manual method of doing this
_________________________________________________
...below is the step by step example using Excel...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.... :-)
- Excel to accompany above
Standard deviation example spreadsheet in excel, just download and save as excel spreadsheet
Ok So What Good is it?
Wiki say;-
Standard deviation may serve as a measure of uncertainty. etc etc and I went WTF does that mean (and I am a statistical / Excel head) http://en.wikipedia.org/wiki/Standard_deviation
The Last Word
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
after all that ..some poetry from Drax..
- Poem - Tomato Boxes
- 6 months ago
- Poem - Living in the Paris Pigalle
- 7 months ago
- Poem - The Peasant Spoon
- 8 months ago
- Poem - The Torture
- 9 months ago
- Poem - Aliens on a Monday
- 8 months ago
- Poem - The Generic Humanoid Carbon Unit
- 9 months ago
More Probability & Statistical Hubs by Drax
- 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%)
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thanks Iðunn
After i read your the page, i'm able to finish my statistic project..thankx dude
hey chopiex_bilaz', no problem.. the power of the Net, isn't it great... cut copy and paste that homework...
th creepy man is realy CREEPY. you should take him off the page.
thanks Chad, yes I must go in for a new identity some of these days
yo folks, I have edited this to show the procedure manually and then using Excel, plus you can go and get the actual spreadsheet if you want and by the way Drax is a poet.... who somewhat ironically likes Excel... *laughs*
Love it, Drax.....the SD calculations, the Excel and the especially the poetry!! ;-)
Hey Mystic Biscuit, great name... thanks very much, I should do more of this Excel stuff some of these days since it is almost a form of relaxation...
..Drax..
awesome man!
thanks KK, I really really must do more of these....
Hey Mndheather - thanks for the comment, Drax...
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....
CD thank you for the great suggestion, I must revise this again... with regard to the 100 I think it relates mostly to incoming hits from google searches, when they are high the score is high so there is a correlation of sorts there....
Thanks Drax...
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... :)
CD and today (Mon May 19th) it is 93.. maybe some of these days I'll sit down and plot this...
thanks Drax..
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.
thanks Sarah... hmmm... as a university academic it might be good to know the distinction between advise and advice.. I like wikipedia, especially because it is not perfect or does not pretend to be. This is much better than say Govt pretending that everything they say is truth....
thnx a lot for such a small and easy way of understanding the standard deviation.
Abhinav I'm glad it was useful to you.... tell others... thnaks Drax
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 Tori, nice of you to say so, thanks very much... Ciao Drax
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.
all right Cem, good that this continues to be useful... thanks for the comment..
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.
Hey Rowan, thanks, glad it was of use to you, I hate that when teachers cannot get the knowledge across...
Can you tell me why it's( Deviation) devided by n-1 but not by just n. What does it really mean?
Hey ES to be perfectly honest I have no idea but I will go and look it up just as soon as I have time and I'll post the answers here within a few weeks..
Thanks Drax
Thank you for sharing the steps to calculate the standard deviation. You rock!
hey great user name, thanks for the thanks regards drax
Thanks heaps for this example! It's by far the easiest to understand. I now understand Standard Deviations! lol.
Hi Matt,
thank you very much for the comment, it is always nice to get encouragement.
Regards
Drax
Chrisssssssssssssss U'r Owsaaaam, U really help me xxxxxx
Thanks. Really helps in schoolwork.
Hey Dots... use the technology... cut that homework time in half... :-)
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.
Hey thanks very much Seb
Regards Drax..
Hey thanks Sexy... ;-) Regards Drax..
hi Drax..... i read alot 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)
thanks man, nice to get a compliment from a Clever Man :-)
great name..
Cheers
Drax
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
no problem Eric, it's great that this hub has proved to be helpful to everybody...
Its really cool way of explaining! This is simple this is useful, you made complex definition to simple and understandable. Good Job.
Hey Areif... thanks for the comment and delighted it was of some use to you...
It doesn't answer the question how to _calculate_. It just tels what the deviation is.
Well No Point... if you read it and follow the 6 steps telling you how to calculate it then you can apply the same rules to any set of numbers... ? so it tells you how to do it step by step...
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
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
Thanks for the comments folks :-)
can anybody tel me the procedure to calculate standard deviation by a calculator...???
Hi Frooty, if you follow the steps 1 to 6 above using the calculator you will get the result...
I can't believe I am looking at the standard deviation formula again. It has been ages but thank you for the reminder though.
Thanks Adorababy... I know when you get away from it you never want to go back unless someone is paying you :-)
Hi! Back to school grade 6! Thanks for helping us go back in time! -- Thanks
Hi ss sneh... glad it was useful :-) ..Drax
its really a gr8 work.. easy to understand..
Hey KP... glad it was of some help... that is all each of us needs.. just a little help :-)
Nice post!! Great work!!
Hey Jha thanks :-)
Great info - Many Thanks for this site
Hi Tony.P... glad you liked it and thanks for the comment :-)
omygosh! thanks so much! Deadline for my stats assignment is tmr and this practically save my life!! huge amount of thanks (: (: (:
Hey Lina... that's great :-) glad it was of some help.. Thanks Drax
thanks so so much, u really helpd me & now i understand
Hey Beauty... good it was useful... :-)
Good information and great hub creation!
Helped me for my Studies ;-)Very Useful Hub!
Your approach towards the statics and maths is amazing!
Thanx for the creation of this hub!
Regards!
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
@submitedgeclb thanks for the very nice comment... keep up the studies... !!!
@Domingo... thanks for the comment, I will definitely come back after Xmas and make more hubs around this theme...
good explaination
thanks Manjusha :-)
Thanks a ton i really learnt more from this dude thank u very very much
Hi Shivaprakash... that's great.. I really really must do more of these... :-)
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?
Hey Savvy although I am tempted to look at this in detail time does permit me to do so at this juncture... sorry mate...
this is simply great! :-) thnx lot Drax!
Hey Besure... thank you for the comment, I'm glad to hear it... :-)
Thanks men... very very simply and clear. Any easier and my brain would have melted lol... Thanks. Lab report, DONE!
Hey Supaman... thanks for the comment.. :-)
Thanks so much Drax! You really made it simple, I finally understand standard deviation!
thank uuuuuuuuuu
@ Janna... that's great that is was useful to you... happy days :-)
@VSK... no probs... my pleasure :-)
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
Hey kully... if you could expand the question a little it would be a big help in trying to answering it...
Such a very interesting information. We are currently studying how to get standard deviation, and it's somehow challenging due to different solving strategies.
MVH... that is very encouraging... to be able to solve a mathematical issue... what else is there in life... :-)
Thanks for this. Very interesting. Nice post!
Plumbing... your url goes to an external source... this is not really cricket... I have resisted the temptation to delete you, this once... join us here at Hubpages share the knowledge and experience...
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.
Hi Skyfire... (great name !!!) thanks for the comment...
Thank you! This helped me organize my chemistry work!
that's good Dani... use the webtech, always... :-)
How do i find the standard deviation using likert scale
Hi Tony... just convert your responses to numbers... if you had the standard Likert - the format of a typical five-level Likert is:
Strongly disagree
Disagree
Neither agree nor disagree
Agree
Strongly agree
number this 1-5
1. Strongly disagree
2. Disagree
3. Neither agree nor disagree
4. Agree
5. Strongly agree
so say 16 people responded;-
q1 3
q2 2
q3 4
q4 6
q5 1
so your series is 3by1,2by2,4by3,6by4 1by5
the data set is then 3 of 1, 2 of 2, 4 of 3, 6,of 4, 1 of 5
so multiplied out 3,4,12,24,5
or you could do it listing them all...
1,1,1,2,2,3,3,3,3,4,4,4,4,4,4,5
so then just take these and proceed from Step 1 and go through the whole deviation process above...
:-)
this didnt work why is it on the internet?
@mrs millis... what did not work,? if you would care to tell me more precisely then I could help you out with whatever part you are not doing right... :-)
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
Well Missunderstood, G'Day to all in Perth.. in order for me to understand what is the question or problem being faced by a reader I often need to ask for clarity, or for clarification, in order to be clear that I am not simply being misunderstood, if you understand...
Yet, understandably the people who often misunderstand or do not return with clarification of their question or tell me what they do not understand are not members of the Hubpages community, they are passers by, they offer nothing, they do not contribute, they are the hyenas/dingos of online society, just flotsam in the great rush of the humanity all carried forward towards electronic understanding...
I assume you have empathy with them and so can understand Misunderstood...
Ciao
Drax
thanks a lot!
very helpful thankx
@Tommy & Matt... thanks very much for the comments, it is always very rewarding when anyone comments.. :-)
thanks a lot author....your explanation is very easy to understand....it is very much useful to me...
Hey Sandy... great to hear that, my name is Drax... from Ireland :-)
nice work. i understand it here more than what i have been thought
Hey Baffa... that is good I am glad, this is always what I find wrong with school stuff, just explain it to me mf... it is your job ;-)
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
Fateme
here is the above as a google doc, just download it as an excel sheet :-)
https://docs.google.com/spreadsheet/ccc?key=0ApwEP
if you need more than this then tell me exactly what you need and I will do my best to answer or give you a working example
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
@ WhiteSnow... Hi thanks for the great comment, I will make a quick hub about using the Excel Descriptive Statistics tool
http://drax.hubpages.com/hub/How-to-Use-the-Excel-
:-)
Hey katie... that's great... use the tech but try and understand it as well... :-)
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
WhiteSnow... so check out http://drax.hubpages.com/hub/How-to-Use-the-Excel-
and for histograms they are easy, go to to Tools, Data Analysis, select Histogram.. input your range as you did before and experiment with the settings to answer the specific question you are being asked..
This is awesome I searched like ten other sites then I found this one. It is definately 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
@ BakerBoy97 ... that's great... I must try to promote it more... tell somebody :-)
@ Abby magnifico !!! I was useless at algebra... I never found a teacher who cared enough to explain it to me properly...
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?
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 :-)
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 :-)
really well and clearly explained, thank you so much! brilliant help to me this was!
Sizz... thank you for saying so, it is appreciated :-)
i absolutely love this after 20 yrs out of school i was unable to have this make sense wow thank you so much!! :)0
Hey thanks Sheshe... I feel that a lot when I cannot understand WTF they are trying to tell me....
Thanx a lot!!! very very awesome. keep it up
Hi FruitySnoops... thanks for the comment !!
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?
@Ronald... good man Ronald, thanks... keeping the old life statistics current is a good habit... !!
Hey PrimaD... good is awesome is good... thanks a lot :-)
Hi Swapnil... good of you to say so... thanks !!
@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
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.
@Deen Mohammad... thanks very much, it is good to know this always !
@Pauline.. thanks for the comment, deviation is a tricky subject and it is always important to learn the fundamental, then you never forgot :-)
@Shiji... thanks very much for the comment, it is appreciated !!
@Lal Nabi... I am very glad that it can help convey what deviation is all about, thanks for the comment !!
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
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 !!
Iðunn 5 years ago
nicely done~