How To Calculate Standard Deviation

First, you need to determine the mean. The mean of a list of numbers is the sum of those numbers divided by the quantity of items in the list (read: add all the numbers up and divide by how many there are).

Then, subtract the mean from every number to get the list of deviations. Create a list of these numbers. It's OK to get negative numbers here. Next, square the resulting list of numbers (read: multiply them with themselves).

Add up all of the resulting squares to get their total sum. Divide your result by one less than the number of items in the list.

To get the standard deviation, just take the square root of the resulting number

I know this sounds confusing, but just check out this example:

your list of numbers: 1, 3, 4, 6, 9, 19

mean: (1+3+4+6+9+19) / 6 = 42 / 6 = 7

list of deviations: -6, -4, -3, -1, 2, 12

squares of deviations: 36, 16, 9, 1, 4, 144

sum of deviations: 36+16+9+1+4+144 = 210

divided by one less than the number of items in the list: 210 / 5 = 42

square root of this number: square root (42) = about 6.48


Paul Edmondson profile image

Paul Edmondson 9 years ago from Burlingame, CA

Nice example. Very easy to understand.

Ole 9 years ago

Yes, exept: you say that you will subtract the mean from every number which in your example is 7, but you subtract the number 6 from every number to get the list of deviations? it is the mean and not the amount of numbers in the list that should be used right?

Wilson  9 years ago

It's quite easy and straightforward. Thanks for refreshing my highschool Maths. I am currently preparing for GMAT exams and i definitely need this review.

Wilson  9 years ago

I am still the Wilson above. Yes Ole you definitely are right. The mean is 7, so we have to subtract the mean from every number. I am sorry i didn't see that. But generally the procedure is easy and straightforward.

sonia 9 years ago Author

Sorry about that oversight - it's corrected now! Thanks for pointing it out.

MaryAnn 9 years ago

I'm trying to pass a stats class to get into a Masters program and this is the only thing that's made any sense so far--THANKS!!!

Amani 9 years ago

Thank you very much... it helped me in performing the calculations of my experiment in this very critical time…!! J

Lex 9 years ago

Thanks! I learned something new!

Ron 9 years ago

Wow! That was new for me!

Adam 9 years ago

Great post! That's what I needed!

Gabe 9 years ago

Nice post! It really helped me!

michelle 9 years ago

Thank you very much for the nice, straightforward info on standard deviations, it totally helped my daughter!

thecounterpunch profile image

thecounterpunch 9 years ago

Do not learn without understanding :)

dajoo 9 years ago

good way to explain

Sophie 9 years ago

Awsome example and walkthrough of SD... it really helped me a lot


Dharam 9 years ago

thanks sonia, you removed my very big confusion by giving live example

thanks once again

john 9 years ago

thanks so much!

AS 9 years ago

Okay, now how do I understand the numbers once I have calculated the standard deviation. Can you provide some examples?

Col 9 years ago

So helpful, thank you. You have succeeded where my Quants professor failed - to explain this in plain language. You don't fancy having a go at Variance for me do you?????

Am really struggling and have an exam next week.

wilfred 9 years ago


isaac 9 years ago

thanks a lot i m having a final exam within 2 days

misho 9 years ago

awesome, thanks!

Linda 9 years ago

Amazing stuff...thanks

Naaman Kipumbu 9 years ago

Great refreshment for me. I'm studying Computer Science and Information Processing with ABMA, UK. Great deal a job!

Trey 9 years ago

Was easier then everything I learned in Stats :-)

Ankur 9 years ago

That's exactly what I was looking for......good work

Ankur 9 years ago

That's exactly what I was looking for......good work

reash profile image

reash 9 years ago


Great hub..Way back in college I was having a hard time figuring out numbers but I managed to find a way though. You must be very good in numbers.

Aaron 9 years ago

right on....i like this site

Kassemi 9 years ago

thanks very much sonia ur very easy

I will use it in building a C# program

Aruna 9 years ago

Thanx for giving me apt solution.

Aruna 9 years ago


d = X- Mean

d2 = d x d


(1-7)= -6



(3-7) = -4



(4-7) = -3



(6-7) = -1



(9-7) = 2



(19-7) = 12


Mean = ∑x/n = Sum(1+3+4+6+9+19)/6 = 42/6 = 7

Therefore Standard Deviation = ∑d2 / (n-1) = (36+16+9+1+4+144)/ (6-1)

= 210/5

= 42

So, Standard Deviation = √42 = 6.48

As per sonia example i have presented with formula & table for exam point of view

Pat 9 years ago

applepie 9 years ago

Aruna, you made it look so simple!!!! I'm sure it is but I am currently in a stats course and having a difficult time making sense of it all, do you have any suggestions where I can get some online help with understanding how to work problems out....thx.

Catherine 9 years ago

The only thing that the example is missing is the following: you haven't articulated where you are testing a sample or a population. If you are testing a sample, then n would be the denominator. However if you are testing a population, you will need to divide by n-1.

sam 8 years ago

does anyone know how to use spss? and do uni level stats stuff??

math penguin 8 years ago

Yes, Sam I am familiar with SPSS. What can I do for you

Chung 8 years ago

yes that's an EASY example, but how do u calculate the standard deviation when there is 20 values and each one is like 5 digits with decimals? it will take like over 10 minutes by hand and for an exam that is way to long for a stdev question. Also, how do u know when to find the population standard deviation or the sample standard deviation?

Lazuardi 8 years ago

thanks a lot! really help me

hannah 8 years ago

that was excellent, very helpful, allowing me to complete my assignment due tomorrow with a little less stress! thumbs up, very appreicative!

Herbert  8 years ago

A bit confused up there about the argument by Ole. What is it? Divide by 6 or 7? The 6 is the number of observations while the 7 is the mean! Can someone help there?

simone 8 years ago

uber helpful...thanks!

Celine 8 years ago

I get the jist of standard deviation but what doees the number at the end show??

(am doing some maths statistic coursework at the moment)


buddy_eagle 8 years ago

thxs... a lot for posting this.... it was a gr8 help

Mikhaila 8 years ago

Thank you so much! I am doing an online course on statistics and this has really helped me.

SXE Chris 8 years ago

thanka a bundle! I had to do an assignment for an anthropology course I am taking at university and this helped me tremendously!! Thanks again, so much!

ISuckAtMath 8 years ago

YA im like doing my homework and i like don't get any of this crap I'm only in like 7th grade... But whatevs, I just wanted to say--OMG UGLY BETTY is on!!!!!!! sry gtg BIBI!!

Celine 8 years ago

What does the final number show? and what can I do with it.. I'm apparently meant to use it to help support my hypothesis that height follows a normal distribution in a school..

Kaitlyn Giammatteo 8 years ago

You made it very easy...thank you!

kashmere 8 years ago

thanks it really helped a quick reference............

rani 8 years ago

what is it with all the fit asian boys

rani 8 years ago

a wanna take 1 home

rani 8 years ago

i'll be rameshes friend

how do you do it in india

can't wait to ring your bell

god............. ramesh your mathes turns me on babyXXX

gagan sharma 8 years ago

thanx a lot lot Sonia....i just forgot how 2 calculate it...u helped me learning it again..great work..

aaron 8 years ago

thank you,quick method

aaron 8 years ago

thank you,quick method

adeel 8 years ago

gr8 example

imran 8 years ago

Good- A very easy way to understand standard deviation

sara 8 years ago

bless had been very useful in answering ma assignment..

loads of thanks:)

Jolene 8 years ago

Thank you soo much!

This helped me out a lot.

AJ 8 years ago

wow, thank you so much! i had been trying for hours to understand the stupid book but your explanation was really easy to understand! great work!

Nontembiso 8 years ago

Thank yo so much Sonia, now I can see the way through my Masters results.

Nontembiso 8 years ago

Thank yo so much Sonia, now I can see the way through my Masters results.

the best 8 years ago

thanks for the great post!

Ash 8 years ago

You've written sum of deviations when it should be sum of squares of deviations...

Neil 8 years ago

Sonia, arent´t you suppose to divide by the number of samples? Why did you substrate 1 from it?

Brian 8 years ago

This is wrong, you don't divide by (n-1), you divide by n.

Pheonix 8 years ago

Thanx very much..... it really simplified everything. thanx again

DC 8 years ago

ITS WRONG.... the Standard Deviation is actually 5.916

BandKid 8 years ago

No, DC, you are found the population standard deviation

Davaine 8 years ago

thnx a lot sonia it reeeeeli helpd me undestand sd... it wuz crucial 4 mii coursework

cagney 8 years ago

thank you so much

Kristie 8 years ago

why don't u just say that the standrad deviation is the root of the mean?

Terri  8 years ago

Thanks! Simplying the steps has really increased my understanding!

CTL 8 years ago


Nice n' Easy!

Marri 8 years ago

Great example

Hiba 8 years ago

Thank you very much . it really helped me a lot!!

Rob 8 years ago

far out, people love ya ..... But it is an excellent, easy to follow example.

The hardest thing about it is trying to figure out what the x and n etc all represent... this example fills in the pieces of the puzzle. Cheers

Suzanne 8 years ago

Thank you soooo much, this has really helped me out, I was at the end of my tether until my tutor recommeded this sight. A few more practise's and I'll be there, I hope! :-)

Bea 8 years ago

Thank you very much for taking the time to explain this in plain English. I am taking my Masters Program and it has been a while since I took statistics as an undergrad.

Marques R. Wilson 8 years ago

I took Stat years ago, the answer here is simpler and I think I can remember and program it. :)

helen udoewah 8 years ago

this has made me a better mathematician i think i will pass my degress stats without tears thinks guys.

jerry 8 years ago

excellent . That was great

Ale 8 years ago

Thank you so much, this really really helped!

venkatesh 8 years ago

Thank you so much, this really really helped!

Peter 8 years ago

Thanks Sonia,

Very informative easy to understand and follow format!

Crossy 8 years ago

Or just use a calculator in stat x mode.

seema 8 years ago

thank you

thats nice explanation with example

Brian 8 years ago

My GMAT study book has a different method for calculating standard dev. Why do you divide by 1 less the number of items in the list in the last step? As far as I've seen everywhere else, this is incorrect. According to my GMAT study book you calculate the mean of the squares you computed in step 2, and the square root the mean.

MAVERICK 8 years ago


ChemQueen 8 years ago

Super super helpful!

vineyl oberoi 8 years ago

thank you very sonia u helped a lot

joanne 8 years ago

Very helpful.....Thanks!!!

DC 8 years ago

Very! Very! helpful

Alyssa 8 years ago

Anyone knoq hoiw to graph it????

mike 8 years ago

this helped a lot. looks like i won't fail my test today!

dizzee 8 years ago

thnk youu really helped!

dizzee 8 years ago

thnk youu really helped!

Warren 8 years ago

I'm still confused

But this is better then my statistics formulas i was given, looks like i'm doing it the long way.

Joe 8 years ago

that was very easy to understand..

thank you

Naungsai 8 years ago

SD is a dreadful tem for me before. Now I understand it clearly.

Willing to see more simple examples of others teams of Statistic like this.

megaman 7 years ago

wow it acctulayy helpped.. thx alot

great example

Judas mesias 7 years ago

man this helpd wid my coursework

thnx we owe u one

Judy Martin 7 years ago

Simplified and quite easy to understand!.... where is my lecturer!

Mike 7 years ago

There are two version

Using n-1 or just using n

If you have a large population you can use n, but for small samples like this you will use n-1..

Kathy 7 years ago

Standard Deviation always confused me this helped a lot.

neel 7 years ago

omg thank you so much. i have this sub who can't teach right and the regular teacher is in chemotheraphy. basically there are no As in the class and very few Bs and im lucky to have a B in it. online helps a lot. thank you

surendra 7 years ago

i have a sirvey in which 1 person choose apple, 2 persons choose bananas, 7 persons choose oranges and 3 persons choose mango. (total 13 persons). i got the standard deviation as 0.862 (from a survey system) and standard error as 0.239.

could some one explain me of how the standard deviation came as 0.862 .

KRISB 7 years ago


Steve 7 years ago

Excellent quickie refresher, thanks a lot

tania 7 years ago

man this is such a help..

thanks man...i really really needed it for

ma hwk...

Jay 7 years ago

Simply Awesome

frank 7 years ago

Awesome. thanks a bunch

Kirill 7 years ago

What if the initial list has negative numbers. For example,

1, -3, 4, 6, 9, 19. Does the answer change and if so, what are the rules? Thanks!

HateMaths 7 years ago

Just to put it out there for any confused people(the only thing Sonia missed out) - when you square the numbers, the minus sign disappears and the result should be a positive number.

Amazingly simple method by the way, even I was able to follow. Thanks a lot =)

Stephanie 7 years ago

Awesome example!!! You scared me at first but once the numbers were there it all made sense....thank you much!!

Kevin 7 years ago

I have a 600 Lvl QDM class and this was is a great refreasher! My text book made it more complicated then it had to be. Great Job! Whew~!

nicole 7 years ago

i still don't you have to make a table or what??

im only in fourth year at school and have my prelims in 3 weeks and im very nervous

i don't get anything to do with standard deviation, means and factorising

my numbers im working on are 45pence 54 pence 59pence 61pence 71pence

i know the mean is 58pence but i dont get the next bit its asking me to do

please help i need it badly




nicole(again) 7 years ago

the way i think i was taught was with a table:S and the middle table added up to 0 or something, i cant find my jotter for it though

if you have time and get round to doing my little sum would the answer be 364?



Warren 7 years ago

Nicole, I will try my best to do your question

Mean: (45 + 54 + 59 + 61 +71) / 5 = 290/5 = 58 Pence

List of Deviations: -13, -4, +1, +3, +13

(List of Deviations is The Mean minus each value (i.e 58 is the mean, so minus 48 pence)

squares of deviations: 169 + 16 + 1 + 9 + 169

Sum of Deviations = 169 + 16+ 1 + 9 +169 = 364

364 is NOT the final answer though...

divided by one less than the number of items in the list: 364 / 4 = 91

('one less' is referring to the mean - 5-1 = 4)

quare root of this number: square root (91) = Which is approx. 9.54

So 9.54 is the standard deviation.

Hopefully that helps.. It helped me to make sure I understand it for my exam tomorrow lol.

kc 7 years ago

the minus one is known as degrees of freedom

martha 7 years ago

hi could anyone help me please I have this big assigment and I really do not understand anything

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Par, Inc., is a major manufacturer of golf equipment. Management believes that Par’s market share could be increased with the introduction of a cut-resistant, longer-lasting golf ball. Therefore, the research group at Par has been investigating a new golf ball coating designed to resist cuts a provide a more durable ball. The tests with the coating have been promising.

One of the researchers voiced concern about the effect of the new coating on driving distances. Par would like the new cut-resistant ball to offer driving distances comparable to those of the current-model golf ball. To compare the driving distances for the two balls, 40 balls of both the new and current models were subject distance tests. The testing was performed with a mechanical hitting machine so that any difference between the mean distances for the two models could be attributed to a difference in the two models. The results of the tests, with distances measured to the nearest yard, are on the next page. A file with this data is also available on blackboard, use it so you do not need to reenter all the samples.


Managerial Report

Formulate and present the rationale for a hypothesis test that Par could use to compare the driving distances of the current and new golf balls. (include why you chose a 1-tailed or 2-tailed test)

Analyze the data to provide the hypothesis testing conclusion. What is the test statistics and the p-value for your test. What is your recommendation for Par, Inc.?

Provide descriptive statistical summaries of the data for each model as well as a histogram.

What is the 95% confidence interval for the population mean of each model, and what is the 95% confidence interval for the difference between the means of the two populations?

Do you see a need for a larger sample sizes and more testing with the golf balls? Discuss.



















































































Whateve 7 years ago

Who knows and who cares!

Hewy 7 years ago

Buddy get a life, were not here to do ur damn home work so don't put a full freakin page of numbers and questions up, sonia awnsered a simple question, take that and go with it b*tch.

Hewy 7 years ago

Martha iz a s1ut. hahahah

Basheer 7 years ago


Janice 7 years ago

Wow! Thanks for clearing this up in english for us new calculators.

Nadira 7 years ago

thanx a lot for explaining the concept so well!!!!!!!!!!!

Lindsey 7 years ago

i have NO idea what u are talking about!!

Camilla 7 years ago


pip 7 years ago

just looking up to remember how to do this, this will make doing my boyfs homework a whole lot easier! i can prob even teach him this!

Tommy 7 years ago

You just saved me a hell of a lot of time on a project that is due tomorrow and possibly just saved my highschool GPA!


mimi 7 years ago

can anyone help me basically i have a report for uni to hand in that requires me to calculate standard deviation and as far as i remember when you take away the number from the mean the total should come to zero, like in the example, but mines is not working. My numbers are things like 6.3 x 10 to the power of 4. I really don't understand what i'm dong wrong. Help!

george 7 years ago

how do you calculate 2 and 3 sigma?

Jade 7 years ago

Thanks i'm currently revising for an exam and this was so straightforward and easy to grasp cheers!

poop 7 years ago

this is the worst advice ive ever seen

softballgirl 7 years ago

that was really helpful sonya thanks

Dianne 7 years ago

Thank you so much for this.

Haterrr 7 years ago

Poop, your name says it all. Your a moron. Sonya provides a good example that has helped many ppl. And thats all you can say is that its bad advice. Get a life...

paval 7 years ago

hey its so easy

Lisa 7 years ago

This was extremely helpful. Thank you so much for posting. This information made finding the SD easy!

Cara 7 years ago

Really helped, thanks!

Elle 7 years ago

Thank you so much! I hope you teach!!!! =))))

Pravin 7 years ago

Thank you hub page this is very easy method to find standard deviation

Pravin 7 years ago

Thank you, this methode is very easy to find out the S.D.

I request you for find out the Standard deviation of the following numbers:


send the answer on my Email ID :

Thank you

Dom 7 years ago

Hey, I am working on my masteres in engineering and was given the std deviation for a test score. I forgot how to calculate it thanks a lot. A few people asked what this means. +/-1 SD is another way of saying where "most" of the people fell in a given popluation if you can assume a standard "Bell" curve. For my example the avg was about an 81 with an SD of 12 this means that ~75% of the people had grades between 69 (81-12) and 93 (81+12). if you are within +/-1 SD deviation of MEAN (avg) you are considered normal or average (on a true bell curve these would be C students but few teachers use true bell curves). I am not as good at giving simple answers as sonia but I hope this helped. BTW Sonia I wish you had been my stats prof.

Pariah 7 years ago

Dom, are your from the UK? If so can you confirm if you ever lived in stockport?

student 7 years ago

well explained! now i know where i went wrong. i should be divided by (#item - 1)

Maizita!! 7 years ago

thanks u saved my math project!!

Stats Exam In 3 days 7 years ago

Great working... very beneficial.. thanks =-)

math_teacher 7 years ago

Quick comment- it doesn't matter if you substract each number from mean values or vice versa as you will square the number in next step so the value will be same.

nima 7 years ago easy to understand.thank you to whomever thought of putting these iranians say DAMETGARM DADASH.

another math teacher 7 years ago

This has been pointed out, but I'd like to emphasize: if you're dealing with a population, then you divide by the number of values; if you're looking at a sample, you divide by n-1. So if the set you're looking at is actually all of the data, it's a population and you divide by the number of values. If you're just looking at a portion, you divide by the number of values minus 1.

Also, there is an easy way to do it on a TI-83 if you have one:

Go to Stat--> Edit

If necessary, clear out L1 by pushing the up arrow until L1 is highlighted, then push Clear and Enter. Then, enter all of your data (push enter between each data value). To get out, type 2nd, Mode (Quit).

Then go to Stat, arrow over to Calc, and choose 1-Var Stats; Enter, Enter.

Sx gives sample standard deviation; the one that looks like ox (with a funny o, which math people call sigma) is the population standard deviation. You have to know which to use.

Very nice explanation, Sonia; I hope this helps, too!

Tamara 7 years ago

Ok wondered if someone on here can help me! Everytime I try to work this out I get a different answer! I have a table of the average time a biological and non biological washing powder took to break down a stain in both soft and hard water. The bio took 15mins in hard water and 16mins in soft water. The non bio took 20mins in both cases. How do i work out the standard deviation from this?

Tamara 7 years ago

Its ok! I' ve just figured it out, i was using the numbers the wrong way round. Thank you for the workings out thought, explained it much better here than anywhere else!

Alice 7 years ago

Thank you sooo much I found this so helpful- Im doing my GCSE stats and this saved me from making a gihugic error with my mean. THANK YOU!!!!!!!!!!!

Concerned Earth Inhabitant 7 years ago

Hey guys, Please try to avoid going in public places like clubs, bars etc for next few weeks. Hopefully this way we can stop the swan flu virus from spreading. Thanks all.

chris 7 years ago

Anyone familiar with confidence intervals? Im studying for the CFA, and one of the learning sections says to calculate the confidence interval using a standard deviation, and the next says to calculate with the standard error.

This must be an error, no?

Brain at ease 7 years ago

Brilliant explanation, Sonya.

You probably just saved my college career.

Brain at ease 7 years ago

Brilliant explanation, Sonya.

You probably just saved my college career.

Sidason 7 years ago

I love your tutorial on SD but there is a slight mistake... when dividing the sum of the square numbers which you would end up with 210 you should actually be dividing it by the number of deviations which is 6 not 5.

MCC 7 years ago

we still dont understand.

we love maths 7 years ago

do not understand

7 years ago

wow very nicely explained. saved me on my test.

Psyturnine 7 years ago

Nicely explained.

BUt yet not helpful.


siuva 7 years ago

very easy,thank u

Paiiige 7 years ago

Thanks, i feel slightly more confident towards my statistics GCSE

Hannah  7 years ago

hey this website is great so glad i came across it just wondering if someone could please clear this up for me i cant remember how to do caculator keeps coming up with numbers such 8.281E-03 when i take away the mean and square it, what does the E-03 stand for?????


gorry 7 years ago

MCC says:3 weeks ago

we still don't understand.

we love maths says:3 weeks ago

do not understand

why u guys so dumb

tonghuyen 7 years ago


tonghuyen 7 years ago

Par, Inc., is a major manufacturer of golf equipments. Management believes that Par’s market share could be increased with the introduction of a cut-resistant, longer-lasting golf ball. Therefore, the research group at Par has been investigating a new golf ball coating designed to resist cuts and provide a more durable golf. The tests with the coating have been promising.

One of the researchers voiced concern about the effect of the new coating on driving distances. Par would like the new cut-resistant ball to offer driving distances comparable to those of the current-model golf ball. To compare the driving distances for the two balls, 40 balls of both the new and current models were subjected to distance tests. The testing was performed with a mechanical hitting machine so that any difference between the mean distanced for the two models could be attributed to a difference in the two models. The results of the tests, with distances measured to the nearest yard, follow.

Formulate and present the rationale for the hypothesis test that par could use to compare the driving distances of the current and new golf balls.Analyze the data to provide the hypothesis testing conclusion. What is the p-value for the test? What is your recommendation for Par, Inc.?










































tonghuyen 7 years ago

send answer for me: my email ""

gory 7 years ago

omg....thats rubbish....i was hopin for sumthin a lil more helpful

thanks 7 years ago

you helped me so much, I was so lost before I read this!

mumbaikar 7 years ago

nice simple and very well presented

very well done 7 years ago

this was very straight forward and easy to understand. Thank you very much!

gigi 7 years ago

Thanks for that brief but straight to the point explanation of getting the standard deviation. I need to know what does it mean by having a standard deviation of 6.4?

Rita 7 years ago

Thank you, Thank you, Thank you, you made it easy to understand!!!!

Alexandra 7 years ago

So much better than those CRAZY sigmas all over the place, and the n and the ridiculous amounts of variables.

Everyone taking AP Stat truly thanks you.

Okta 7 years ago


Sarah 7 years ago

Thank you so much! You condensed an hour long lecture into a few simple steps! It is truly amazing how quickly...or slowly a professor can throw simplicity out the window!

please clarify 7 years ago

You really should clarify in the text that you are calculating a sample standard deviation, and not a population standard deviation. Because it is 5.92 for the population standard deviation. (210/6=35; sqrt(35)=5.92)

jaised 7 years ago


lisa 7 years ago

wonderful thank you for helping me understand

sage 7 years ago

very helpful

Elijah 7 years ago

im taking math at syracuse university and we are learning standard deviation. my teacher explained this so horribly that i didn't understand it. this made it soooo easy for me to understand. looking at this, i litterally learned it in 1 minute

Sabrina 7 years ago

Fabulous article. I'm working on Data Management homework and this has really helped me understand it! Amazing job.

Candace 7 years ago

This helped A lot!!!!!!!!! :]

Malori 7 years ago

yea this reali helpd been stuggln with standard deviation for a while

Viola 7 years ago

Thanks a lot Sonia...!

Asar 6 years ago

Thanks a lot. This made things so must easier for me. Now why teachers do it this way.

Jason 6 years ago

I Agree with asar, if teachers showed us it this way i think no one would have a problem of understanding!! thanks.

thank you sonia 6 years ago

any one care to explain this step? "divided by one less than the number of items in the list: 210 / 5 = 42"

is it because you're calculating the avrg standard deviation of all the nos. from the mean, that's why you do this ? or..?

kirk 6 years ago


mayyam profile image

mayyam 6 years ago

thank you, this was very helpful.

i've never had a teacher that explained it this way. they over complicate things and then wonder why the class average is a c.

Kamal 6 years ago

Great Job Sonia!!!

Rob from Canada 6 years ago


Zeeshan  6 years ago

i have a question please i wil appreciate if any1 help me in it

Mean and the S.D. of a set values is 100 and 5. compute mean +-2 S.D. and Mean +-3 S.D.. alos we have to interpret the results in the light of empricial rule and chebychev's inequlity

jl 6 years ago

how do you know whether you are calculating a sample or a population deviation?

jl 6 years ago

how do you know whether you are calculating a sample or a population deviation?

jl 6 years ago

how do you know whether you are calculating a sample or a population deviation?

pojong 6 years ago

please help me to calculate below question

x 0.06 , 0.01 , 0.01 , 0.00

y 0.01 , 0.08 , -0.13 , 0.01

z 0.01 , -0.13 , 1.16 , -0.08

t 0.00 , 0.01 , -0.08 , 0.01

What is the standard deviation in the determination of x,y,z

and origin time

pojong's mom 6 years ago

hey you come on internet and try to get someone to do your homework. Pojong you are very very bad father is waiting for you!

calvin 6 years ago

THANKS! I needed this to calculate error for my calibration curve in my lab!

Hamza 6 years ago

thanks this helped a lot :)

李村 6 years ago

Kait 6 years ago


Much easier than the formula my stat teacher provided.

StrifeHart 6 years ago

Thanks SO much, you explained it such better than my math text did.

hgfiY Jffdlax 6 years ago

EVADALI 6 years ago

Sonia, all I can say is that I freaking love you!! Thanx for making it sooo easy!!

sudeera 6 years ago

really nice...thanks

Bob 6 years ago

Okay. I don't know if this was already answered in the comments as i don't want to read through all of them. There are two types of Standard Deviation. One is Population and the other is Sample. This article highlights the use of

When you are calculating the population standard deviation (when all the numbers in the set are all of the values [30 people take a math test, and you have 30 values]):

you divide by the total numbers in the data set (in my example, 30)


When you are calculating the sample standard deviation (300 people take the ACT test and here are 15 of the results):

you divide by one less than the amount you have (in my case, 14)

Bob 6 years ago

oops. i didn't finish my sentence. this article uses sample standard deviation

aline 6 years ago


but why did you divided by one less than the number of items in the list?

is it related to a sample or population?

cause ive seen other examples and they just divided it by the numbe of items in the list

A. Rajendra  6 years ago

It is very easy to understand.Thank you f for giving simple example.

Venosa 6 years ago

It is very easy to understand.

snickers 6 years ago

I cant believe this actually helped me. Thanks...I hope I pass my test that I have tomorrow cause of this

RANA 6 years ago


mz.hughez 6 years ago

omg!!! Thanks sooo very much, this make so much sense and I got the right answer the first try. I'm taking stats after being out of highschool over 10 years ago. Thanks a bunch!!

Supriya 6 years ago

Nice example but why to substract 1 from the no of items in the list. Please tell me why variance is square & standard deviation is a square root of variance. I mean to say how to apply in a practical sense.

Marvinmasterpiece 6 years ago

Thats the has been there before you were born.why ask why?

King 6 years ago

thank you whoever you are. Made my day a hell lot easier

Sandip 6 years ago

Its Very Very Simple Method To Understand For We INDIAN Students.. Thanks A Lot..

lisa 6 years ago

OMG been tryin 2 make sense of sd 4 wks u just helped me do it in 15 mins ne 1 tnx

ash 6 years ago

thankyou so much :D

mason 6 years ago

had enough of stats all together. thanks i guess my question wasn't aboust sd after all. still confused in the VA

Wilson 6 years ago

still the wilson from above. I was wrong in two aspects of my calculations. The geneRAL PRINCIPLE IS THAT I AM A DOUCHE REMEMBER THUS

Vishal 6 years ago


thanksalotsonia 6 years ago

thanks a lot sonia. very helpful

Ruthie 6 years ago

hey! thanks a lot your explanation was quite clear,thumbs up!!!

Brandy 6 years ago

Thank you so much, this is the only site of been to that actually makes sense. Very straightforward and informative.

Ruthie 6 years ago

This is awesome, love it! I'll just add a small correction, if you don't mind... Where you say "sum of deviations" you should say "sum of squared deviations." Thanks for this nice work!

future pharmacist 6 years ago

Perfect thank you so much

Ira Sharma 6 years ago

thank saved me in my corporate finance class..:)

Gabriel Ma 6 years ago


you saved me from my maths test =))

Kevin 6 years ago

Thanks for helping me finish my thesus.

Ariel B. 6 years ago

Like Kevin up there, I'm working on my thesis as well! This explanation was so simple and so easy. Thanks again for your help!

felix 6 years ago

you made it look very easy. I will need a stat book if you have made one.

Manna in the wild profile image

Manna in the wild 6 years ago from Australia

Good. Well done - that was short and simple.

Sonny 6 years ago

omg thank you i was trying to work this for hours.. but this was a great help.........THANK YOU

hungarian girl 6 years ago

Please help me: how can I calculate standard deviation from these datas?

Number of TV sets owned:0,1,2,3,4,5

Frequency: 1, 32, 32, 20, 7, 3

Thanks a lot.

tokcha 6 years ago

Thanks for your help,simple is always the best!

LOL 6 years ago

LOL, this shit is shit..the worst inaccurate shit i have ever seen

Ally 6 years ago

What if ur given at grouped dat, does it apply the same formular, b'cos my lecturer told me that, when ur finding SD for un grouped ur using the same system as explained here bt for grouped u have to divide the X-square x the frequency, then u proceed,

Craig 6 years ago

Great example of Standard Deviation. Appreciate the help, thanks!

TB 6 years ago

Such a good example and explanation of standard deviation. thanks for this!

DANIELLE! 6 years ago

thanks this helped me make a brochure for my math final . you know how to explain it way better then my ignorant teacher!

Janna 6 years ago

Thank you sooooooooooooooooo much I have been trying to figure this out and it was driving me crazy this helped me so much

Pete 6 years ago

Very nice explanation and example. I'm going to learn statistics for the first time at age 72 and this is a great help. Thanks.

Nayef  6 years ago

hey Sonia... great job but this is only works for a little bit of numbers... use this it's better:

for discrete [(b-a+1)^2 - 1]/12

for continuous (b-a)^2/12

*note: b= largest number , a= lowest

weird 6 years ago


Taya 6 years ago

Thank you soo much i had a big exam the next day and i couldn't understand Standard deviation. This helped a lot THANK YOU!

ba 6 years ago

great help better than the online instuctor

Tassy 6 years ago

OMG - I no wat im going

wowwwww 6 years ago


Proof Reader 6 years ago

Sonia, well done. i could easily follow your explanation. Thanks for posting the example.

N.Ashok kumar 6 years ago

Thanks a lot ... this is very helpful for me thanks a lot...

N.Ashok kumar 6 years ago

i hav one problem i need to calculate process capability for a mchine using these data plz anyone can help me... the data is lik this 5.24,5.22,5.22,5.22,5.22,5.22,5.23,5.22,5.22,5.22,5.20,5.21,5.23,5.20,5.22,5.22,5.22,5.22,5.20,5.22,5.22,5.22,5.22,5.22,5.22..... please help me

Abbott 6 years ago

Q.E.D. "Quite Easily Done."

Provas Sarker 6 years ago

impressive i got it worth learning.......thanks

Dale Hafner 6 years ago

OK, got it. The statistical calculator in the software program I am using offers 3 standard deviations to adjust some alarm limits. Is it just mulitplying the value by 3? Therefore 3 SDs in the example given above would be 6.48 X 3 =19.44. Correct or no?

Miroslav 6 years ago

I built a website uding this Method and its 100% correct

Miroslav 6 years ago

Hers the link to the website i built on this

Sarah 6 years ago

Wow, thank you! This is my second Stat class and the only thing that has made sense.

prashant 6 years ago

thanks!! i have my GRE paper tomorrow!! and this helped me

Steve 6 years ago

Taking my GMAT in 2 hours. This probably saved a few points for me. Thanks!!!

angie 6 years ago

Thanks,You made my day

karimeldib profile image

karimeldib 6 years ago from Dubai, UAE

hi all,

Why i am getting 6.34 instead of 6.48

Femi 6 years ago

This is quite straight forward

sugar 6 years ago

this is really perfect! thx sonia..i gt 6.48 too

Smurf 6 years ago

Thanks man!

means a lot to know there are people like you out there that are willing to help others like me.

Jason 6 years ago

Much thanks !! very helpful.

Nivedita 6 years ago

hey helped me a lot

Abbas Muneer 6 years ago

It's quite easy and straightforward. Thanks for refreshing my highschool Maths

Msc.BioStatistics 611 (p.u) (Abbas Muneer) 6 years ago

Good thank u

It helped me a lot.

sullivan anye ade 6 years ago

Whoever did this...u a genius in explanation

giirll89 6 years ago

thanks u saved my life! stats exam in 12 hrs!

Kdukpa 6 years ago

Thanks for the posting and everybody's comments. I just had statistical class and this has helped me greatly.

Thanks a lot again.


tankz bro.....

itz very easy to catch up

baylorbear 6 years ago

THANK YOU. I HATE stats and this is the only thing so far that has made any sense. This one minute of reading has explained much more than my professor could ramble about for an hour.

kevin 6 years ago

There is an online tool to calculate std dev:

rach 6 years ago

this really helped me with physics homework for my lab due tomorrow morning, thanks!!

aayush  6 years ago

thanks lifesaver :)

watch harry potter the deathly hallows 6 years ago

So happy I found this!

Tony 6 years ago

Very easy to follow. thanks.

bang  6 years ago

any body know the explanations for the equation. like why or how it was found. THE PROOF. 8th grader

Armon 6 years ago

Thanks this was very useful

James 6 years ago

I finally understand :D, I hope this works for that Russian theorem as well as empirical rule thing

Steph 6 years ago

Thank you, this post was so helpful, and I feel like I actually understand. I wish my stats professor could explain it this easy : )

maegan 6 years ago

what a great post!

i can A's my test in stats cause that's the only lesson that i'm confuse of... if our prof. give us some quiz, i often cheat!!!hahaha...

Renee' Roche' 5 years ago

Wow I Actually Understand How To Do This Now! Thanks!

noula 5 years ago

very useful :) thanks

Paul 5 years ago

Isn't except spelled with a "C" in it OLE?

Your first response to sonia says yes exept....or am I not reading it correctly?

Midoryu 5 years ago

So...what about significant figures?

abbas muneer 5 years ago

very informative and useful thanks

Abbas Muneer Msc.Biostatistics 611-09 p.u

abbas munir 5 years ago

its help me a lot thanks

Abbas Muneer Msc.Biostatistics 611-09 P.U

abbas muneer 5 years ago

its makes me easy thanks

Abbas Muneer Msc.Biostatistics 611-09 Punjab Univesity

abbas munir 5 years ago

thanks its so easy

Abbas Muneer Msc.Biostatistics 611-09 Punjab Univesity

camilla 5 years ago

very helpful =)

Bob Segar 5 years ago

Get a life losers!!!

Lesley 5 years ago

thanx for taking your time to help other in need.

Meena 5 years ago

thank you so much!!!

Jack 5 years ago

Well in, quite a good explanation!

thinker 5 years ago

u guys r so good

Abbas Muneer ( Msc.Biostatistics 611-09 Punjab Univesity ) 5 years ago

thank you

Abbas Muneer Msc.Biostatistics 611-09 Punjab University.

AbbasMuneer 5 years ago

thank you

Abbas Muneer Msc.Biostatistics 611-09 Punjab University.

Tyler 5 years ago

thanksssss! :)

Maria Hernandez 5 years ago

Thanks this really helped me with my math homework! i got a good grade on it! so thanks again! ;)

Ruo 5 years ago

The examle is straight forward and easy to understand. thx a lot. ^^

john 5 years ago

what if you are given a sample mean of 82, a variance of 112.5, and n=45

Ansari 5 years ago

It was really helpful, and pretty easy to understand, thanks :)

Varun 5 years ago

Thanks a lot! That was the simplest and easiest method of computing SD. Thumbs up!!

tyrellb 5 years ago

i am currently doing an independent research project, and my teacher failed to teach me how to do SD. this was very helpful for computing SD! thanks a bunch :)

ZAM 5 years ago


samad 5 years ago

hello,thanks,this help me a lot on my exams,thanks.GOG may bless you

Stephen 5 years ago

This helped me so much. Having a teacher with a heavy spanish accent sucks. Im coming here for homework.

JavaKid 5 years ago

can anyone here help me how to estimate mean and standard deviation for group data using ogive?

shazny 5 years ago

tanx broder ....this was helpful

syed 5 years ago

Thank you very much.....this helped me a lot when i had no time and no one there to help me out



Iqra University- Karachi Pakistan

Reddevil 5 years ago


Water 5 years ago

Thanks a lot, helped in my biology practical after I forgot to bring my books! Good work. :)

baris 5 years ago

excellent tutorial, understood in 10 seconds... other links were crap when I googled it !

beer 5 years ago

Thanks a lot.

face 5 years ago

Thanks, helped a lot!

dadah 5 years ago

thanks sonia..:)it helped me to answer my big assignment.. kip it up

TJ 5 years ago

AWESOME!!!! Great POST! gonna pass my test now... lol

thanksalot 5 years ago

i could never understand this in class and this really made it so simple

mad 5 years ago

thanks so much! i hate when you can never understand math but this made it so simple.

nathan 5 years ago

what does sd mean to the data?

santosh 5 years ago

it's Nice

Holger 5 years ago

thanks you made it sooo much easier to understand,than these complicated stats books.!

hno 5 years ago

than you so much

now i need ouation about t-test

Gralenite 5 years ago

kool example

jayant 5 years ago

very good and neat explination guys

Jordie 5 years ago

Thanks! :)

jae 5 years ago

huh i just started math and i cant understand

plz explain further

Lorrie 5 years ago

Thanks for putting this out there to help others.

Fendi  5 years ago

Wow, very helpful. I was given a complicated formula to do this but this procedure made it so much easier! Thanks!

karleena 5 years ago

Thanks, any layman can easily understand how to calculate standard deviation!

Dan 5 years ago

Helped me a lot, thaaaaanks heaps!

stevo 5 years ago

Thank You sooo much, you def saved my college career!!!

selena 5 years ago

thanks for posting this whoever u are. twas helpful.

reb 5 years ago

Thanks so much for your help! :D

brilliant 5 years ago

u all are so pathetic ,u find this stuff tough ,shame on ur mathematical aptitude,learn sth from indians.

Fembi 5 years ago

This does what millions of stat teachers have been unable to do in decades!

Vinayak 5 years ago

Thank You, this was very helpful.

5 years ago


5 years ago


Jonys 5 years ago

I am doing a QM case and it has helped me

|Trimbo 5 years ago


DGOZZLE 5 years ago

what does the standard deviation actually find out

kissmychicken 5 years ago

yeah what does standard deviation come out with DGOZZLE

kissmychicken 5 years ago

yeah what does it actually find out. HELP!!!!!!!

M Asif 5 years ago

Interesting, Thanx

kissmychicken 5 years ago


lorry 5 years ago


I have read all f the above, but can't figure out what to do if I already know the standard deviation. Here is my problem:

A supplier of lumber for home building sells construction-grade 2-by-4 lumber in 8-foot lengths. Because of irregularities in the wood and shrinkage caused by drying, there is some variation in actual length. Lumber is acceptable if it is between 95.5 and 96.5 inches. The current process produces lengths that are normally distributed with a mean of 96.04 inches and a standard deviation of .52 inch. Is this process capable of meeting standards of acceptability?

How do I figure this out?

sarah 5 years ago


siobhan 5 years ago

erm... negative six squared would equal negative 36? not 36?

siobhansaretard 5 years ago

lawwwwl @ above comment. think realllllllly hard about what happens when you multiply 2 negatives together genius....sooo.....ermmmm....urafuckingidiot.

poopster 5 years ago

the comments on here are hillarious...

Benster 5 years ago

Ahhhhh this helped me!

mattias 5 years ago

so freaking confusing. sorry my math teacher can teach better than this and she sucks crap. sorry, but you need to be able to write this better so kids can actually understand

matias 5 years ago

not really its easy to understand

dick penisten IV 5 years ago

mattias ur fcking stupid. u in special program or something? this sht is easy like ur mom. god ur retarted

kira 5 years ago

what the hell that wasn't my damn question

br3t 5 years ago

Just got some more points on my exam! thanks

Oluwalana Mike 5 years ago

Its a gra8 help to me. TXS

Avneel 5 years ago

Very nice example, thanks

hey 5 years ago

but the answer is wrong. should be 5.91 sth... cos it's over 6, not (6-1) i.e. 5 for step 6.

C2W 5 years ago

For me,it is the easiest and the best tanx...Good work

Qasim 5 years ago

Sonia! Thank you...

lenieke 5 years ago

Hey great, many difficult explanation on the web, but this example makes sense :)

jesereth 5 years ago

It was simple yet helpful information. Thanks!

Adham 5 years ago

Thanks for the easy to understand example; I just have one wonder which I am clear about:

Why we need to divided by one less than the number of items in the list: 210 / 5 = 42??? Is it just the role; to always divide the total of all deviations by one less than the total/sum of all items in the list? Please clarify.

Thanks a lot,


ELVIS SHIVHALO 5 years ago


Dennis 5 years ago

Hey thnx I was very impress with d way u explained SD

:) 5 years ago

Thanks. Helped out tons

madds 5 years ago

omg thank you so much!! this is great!

Sunday John Bosco 5 years ago

I have got the point but why do you "divided by one less than the number of items in the list" I am confused there.

Magarac 5 years ago

Wow Sonja, you rock. YOU should be teaching my Statistics course, not the doofus who's getting paid by my university to do it! :-)

Thank you!

Statlover 5 years ago

that method is epic so cool

it is sorta different in school. This is nice and easy.

mars 5 years ago

wow, lot of comments on here.

Andrea Noisternig 5 years ago

Oh my god, soo good explained! If only all math teachers could be that detailed.


cin 5 years ago

it's very clear thank you sooo much!

Melissa 5 years ago

Just wanted to add to the long list of THANK YOUS! Doing a bloody stats unit :)

Deedee 5 years ago

That formula had me soooo confused but you made it so simple! Thanks so much!

Samuel 4 years ago

Thanks a lot. i passed my test thanks to you.

irene 4 years ago

I can my exam comfortably thank you Sonia

Amanda 4 years ago

I totally prayed to understand how to calculate standard deviations and found this site! AMAZING example!!! I could not understand how to calculate standard deviations until reading this right now! Love it, thanks a bunch! Jesus is AWESOME!

zainab 4 years ago

That is exactly what I was looking for!!

Thanks a lot :)

Esther Ripplinger 4 years ago

I agree with the other one who said,"This is exactly what I needed!" I misinterpreted the formula. It left me wondering, but walking me through it is exactly what I needed. Thank you!

Jeff 4 years ago

The description was simple and the example you provided helped tie it all together. Great job.

emma 4 years ago

wow! awesome! you're AMAZING

kaye 4 years ago

Thanks for that explanation, you make it sound so easy, i am currently doing an Ass. Deg. and this statistics is killing me, but u certainly cleared that up for me, by the way after doing all of that what is the next step.

AngaNaa 4 years ago

OMG!!!! Thank you SO much. This was very helpful and now I can work on mastering this technique for my Operations Management Test that is coming up. I had forgotten how to do standard deviations and lost my notes from my statistics class to refer back to it! What a life saver!!

Lee 4 years ago

Good Job, Thumbs up from me, needed clarification i was doing this right, and you did a great job of it

Anon 4 years ago

well there is a catch. we only divide by one less than the numbers in the list only if our list is a sample. we divide by the exact number of items in our list if our list is the population, not a sample

Prasad Ajinkya 4 years ago

We have written a post on how Standard Deviation is applicable in Finance, especially when doing an analysis in Excel. Do check it out -

Comments and feedback invited!

Musa simon 4 years ago


Dabee 4 years ago

I need some one to help me how to caculate SD when i have 2 value in a sample

For exemple:

A=3.3 and 3.5

B=3.2 and 3.4

C=3.4 and 3.4

D=3.3 and 3.1

If some one know please help me and send me the formula on my e-mail address as

Thank you very much

gangsta 4 years ago

omg its thugtastic yo

Maria 4 years ago

THANK YOU SO much! I have an exam tomorrow and ALL semester I NEVER got it until now :)

Max 4 years ago

Thank you very much.

Ikram Ahmad 4 years ago


easin 4 years ago

thank u so so so so so so much

4 years ago

can the standard deviation and the range of a set of data ever equal??

hehehehe 4 years ago


The example school gave was kind of confusing, and when I was reviewing I couldn't understand.

SATHISH 4 years ago


Buddy 4 years ago

I'm sure it's been mentioned but I didn't read every post. This is the method for finding a sample standard deviation. If you're finding a population standard deviation you divide by the number of observations, not n-1.

Hetty 4 years ago

Thank you for this!

Helped me with applied science coursework!

SUCK MY EAR 4 years ago


In otherwords, this is EPIC POTATO :)

Devon 4 years ago


I do your mum 4 years ago

No one will me read my comment;)

Jye 4 years ago

Thanks so much. Helping out my year 12 math.

Sarah N 4 years ago

The only reason I will be passing my stats test tonight is because of you! Thank you so much. I wish my teacher could break it down like this :/

Lene 4 years ago

that was awesome.

short,sweet,to the point. AND easy to understand.

EE 4 years ago


ganesh 4 years ago

X f dx dx2 fdx fdx2

40 12 10 100 120 1200

Here every thing i understand 3rd raw dx i don't understand any body help for this...

Garry 4 years ago

Superb. Nice and easy to follow, thank you

yuva 4 years ago

very interesting and nice example thank u

ellie 4 years ago

Thanks!!It was easy to understand because you broke it down step by step THANKS for the help!!

geezel 4 years ago

thank you so really helps me.

Anil Singh 4 years ago

Thanks Sonia. Now i can say its simple to calculate SDEV.

Math is terrible 4 years ago

Thank's Sonia! God bless you! It helped a lot when i did my math homework!

thanks this kinda helped 4 years ago

this was pretty good

Drax profile image

Drax 4 years ago from NYC....

Olivia 4 years ago

Pls i have this assignment help me. 55+53+80+53+56+90+70+78+80+85 in a standard deviation

Apples 4 years ago

55 53 80 53 56 90 70 78 80 85

Mean = 700/10=70

difs = 15 17 10 17 14 20 0 8 10 15

squares of difs = 225 289 100 289 198 400 0 64 100 225

sum of squares of difs = 1890

sum of squares of difs/(number of things-1) = 1890/9 = 210

standard deviation = root(210) = slightly less than 14.5

Do not hold me to mathematical accuracy, I am not currently with a calculator (hence the approximation of the final answer)

Apples 4 years ago

You should verify that this is the formula that your class is using though, another common version divides the second part by just the "number of things" instead of "number of things - 1".

This gives us 1890/10=189

root(189) = 13.something, probably around 13.7.

Jonathan 4 years ago

Is 42 the variance in this case?

Daina 4 years ago

thanks 4 such a great effort itx really help 4 d readerx

Math Gal 4 years ago

this is incorrect!

you do not divide by one number less than the number of items in the list, you divide by the number of items in the list.

the correct standard deviation for this problem is approximately 5.916.

Afshan 4 years ago

awesome!!! you're the man!

Nunu Norbert 4 years ago

u just saved me from failing my stats examx thanx a lot

Tommy 4 years ago

Thank you, OMG

Dawnysha 4 years ago

Why do you divide by 5 and not 6? (at the end)

RESPECT BOY 4 years ago


michaelheemson 4 years ago

hi there tommy if your still knoking around i think this is the contact

and some info , they have a deal on at the mo , mention michael hiltams put you on

sean 4 years ago

cheers, very easy to understand

FOSTOM 4 years ago



Lee 4 years ago

I would like you help me about my final report free test. I don't know how can I do students deviation or standard deviation below:

360 all of students for free test in final report

108 group of sample in final report

score of group sample for free test there are 15 questions.

list of students score:

22 students got 1 score

23 students got 2 score

30 students got 5 score

10 students got 7 score

10 students got 9 score

10 students got 13 score

3 students got 15 score

Please use determine the standard deviation by using the function bellow:

SD= ?(( N?fx^2 - (?f?x)?^2) )/?( 2@N))

MiddleSchooler 4 years ago

I find it interesting everyone seems to be in high school or going into college. I'm in 6th grade and learning this. Lol, too many big words from other websites. I CAN FINALLY GET MY HOMEWORK DONE! Thank you.

lauren 4 years ago

Thanks so much! that was easy to understand

ben 4 years ago

no thats wrong you don't divided by one less than the number of items in the list you just divide by the same number of numbers in the list

that the right way.

Lucy 4 years ago

Thank you! I completely understand now. Based on the comments, it seems like lots of people are doing this in High School maths. I wonder why we need it in 6th grade maths? Also, is there a real-world use for standard deviation?

kabirdes 4 years ago

The explanation was Awsm sonia :)

Can u plz explain where do we use it..?

Sal Stephens 4 years ago

You rock Sonia! Great explanation!!!!!

agabrans 4 years ago

I'm trying to figure out this problem from school. Your explanation of Standard Deviation was awesome. I seriously understand it now! Is it possible to figure out this problem? I don't see the mean or list of numbers that I THINK I need. Thanks!

You have collected 11 water samples. The variance of the sample is 47.3084. What is the standard deviation of the sample (4 decimal places)?

Andrew Laughton profile image

Andrew Laughton 4 years ago

Thanks so much for the explanation!

Vincent 4 years ago

YEs i finally knows now

thegoofyblue 3 years ago

omg this is the best thing ever! THANK YOUUUUUU

roboporno 3 years ago

every calculator i go on says when i square a negative it comes with a bigger negative, help?

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InterestCaptured 3 years ago

This is perfectly explained, thanks a lot

hanaa ibrahim 3 years ago

i have a question says : if the standard deviation of the numbers X1, X2, .....,Xn is 4 , find the standard deviation of the numbers : X1 -2, X2-2,.....,Xn-2

Trevor 3 years ago

agabrans, it is 14.2640

Ramin 3 years ago

Thanks a lot saved me the test :D

nkiran 3 years ago

I don't understand why to divide the sum of squares by "by one less than the number of items in the list" and not by "number of items in the list". I find the latter logical.

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Goldenserenity 3 years ago

Thank you! I read the chapter on this in my math book and I didn't have a clue. I went through your post once and I understand it. You are awesome!!

Jack Knowell 3 years ago

Its interesting wish it was explained with some graphics and more examples as it was explained on

bastillandude 3 years ago

how could i compute the standard deviation of this data

no. of respondents

survey 3 - Very 2 - Satis 1 - Poor

question good factory

1 40 2 0

2 38 2 2

3 37 5 0





i need asap



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calculus-geometry 3 years ago from Germany

Just noticed my statistics tutorials are getting a lot of incoming visits from this article. The comment thread here is 100 times longer than the actual hub, lol.

sigmund 3 years ago

very helpful. thanks.

Shannon 3 years ago

THANK YOU! This has been the first time in over a year I have been able to understand this!!

sarDeemsgen 3 years ago

We helpful to obtain at the top of living however as of late We have developed a new opposition.

Quintana 3 years ago

If you calculate the standard deviation by hand, you will likely end up having to use a calculator anyway for the last step in computing the square root. So why not just use a calculator for the whole thing?


At least you can avoid computational errors. The only errors you might make are in entering the data. While it's good to know the general method and formula for standard deviation, I don't think calculating it by hand is practical or wise for a set with more than 10 numbers. You can also use something like Excel or Calc (open source spreadsheet program that comes with Open Office.)

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paxwill 3 years ago from France

It just goes to show you how much emphasis search engines place on old content. This hub shows up higher in searches for standard deviation because it's over 6 years old, but there are much better s.d. tutorials on HubPages, even if they happen to be younger.

For instance, this hub doesn't explain the difference between population and sample s.d., that is, when you divide by n and when you divide by n-1 before taking the square root. Here are hubs that offer better explanations:

Krishley 3 years ago

Calculating standard deviation is not really difficult but can get quite complex when you have lots of numbers. I'm currently preparing for my A-Level statistics paper and i use this calculator to check my answers : http://standard-deviation-calculator.en.softonic.c...

rj 3 years ago

thanks fr the help

hmm, 3 years ago

divide by n or n-1?

rebecca 2 years ago

perfect explanation. thanks

PRINCE 2 years ago

Thanks to my virtual tutor, simplicity is the ultimate sophistication

rebecca 4 weeks ago


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