# 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

## 472 comments

Nice example. Very easy to understand.

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?

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.

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.

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!!!

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

Thanks! I learned something new!

Wow! That was new for me!

Great post! That's what I needed!

Nice post! It really helped me!

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

Do not learn without understanding :)

good way to explain

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

Thanks

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

thanks once again

thanks so much!

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

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.

hello

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

awesome, thanks!

Amazing stuff...thanks

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

Was easier then everything I learned in Stats :-)

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

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

Hi

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.

right on....i like this site

thanks very much sonia ur very easy

I will use it in building a C# program

Thanx for giving me apt solution.

X

d = X- Mean

d2 = d x d

1

(1-7)= -6

36

3

(3-7) = -4

16

4

(4-7) = -3

9

6

(6-7) = -1

1

9

(9-7) = 2

4

19

(19-7) = 12

144

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

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.

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.

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

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

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?

thanks a lot! really help me

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

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?

uber helpful...thanks!

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)

thanks

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

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

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!

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!!

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..

You made it very easy...thank you!

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

what is it with all the fit asian boys

a wanna take 1 home

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

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

thank you,quick method

thank you,quick method

gr8 example

Good- A very easy way to understand standard deviation

bless ya..it had been very useful in answering ma assignment..

loads of thanks:)

Thank you soo much!

This helped me out a lot.

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!

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

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

thanks for the great post!

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

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

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

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

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

No, DC, you are wrong...you found the population standard deviation

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

thank you so much

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

Thanks! Simplying the steps has really increased my understanding!

:)

Nice n' Easy!

Great example

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

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

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! :-)

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.

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

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

excellent . That was great

Thank you so much, this really really helped!

Thank you so much, this really really helped!

Thanks Sonia,

Very informative easy to understand and follow format!

Or just use a calculator in stat x mode.

thank you

thats nice explanation with example

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.

GOD BLESS YOUR SOUL!

Super super helpful!

thank you very sonia u helped a lot

Very helpful.....Thanks!!!

Very! Very! helpful

Anyone knoq hoiw to graph it????

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

thnk youu really helped!

thnk youu really helped!

I'm still confused

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

that was very easy to understand..

thank you

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.

wow it acctulayy helpped.. thx alot

great example

man this helpd wid my coursework

thnx we owe u one

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

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..

Standard Deviation always confused me this helped a lot.

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

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 .

THANKS!

Excellent quickie refresher, thanks a lot

man this is such a help..

thanks man...i really really needed it for

ma hwk...

Simply Awesome

Awesome. thanks a bunch

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!

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 =)

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

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~!

i still don't understand..do 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

thankyou

nicolee

x

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?

nicole

x

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 - 1...so 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.

the minus one is known as degrees of freedom

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.

Assignment:

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.

Current

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Who knows and who cares!

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.

Martha iz a s1ut. hahahah

Excellent

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

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

i have NO idea what u are talking about!!

WHAT????? I'M GOOD AT MATHS AND THIS MAKES NO SENSE...I'M SO CONFUSED....:s

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!

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!

THANKS A MILLION!

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!

how do you calculate 2 and 3 sigma?

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

this is the worst advice ive ever seen

that was really helpful sonya thanks

Thank you so much for this.

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...

hey its so easy

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

Really helped, thanks!

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

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

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:

-1.0628,-1.0857,-1.1169,-1.1443,-1.171,1.1981,-1.2254,-1.253,-1.2808,-1.309

send the answer on my Email ID : pravin.hudge@yahoo.com

Thank you

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.

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

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

thanks u saved my math project!!

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

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.

woww.so easy to understand.thank you to whomever thought of putting these examples.as iranians say DAMETGARM DADASH.

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!

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?

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!

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!!!!!!!!!!!

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.

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?

Brilliant explanation, Sonya.

You probably just saved my college career.

Brilliant explanation, Sonya.

You probably just saved my college career.

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.

we still don't understand.

do not understand

wow very nicely explained. saved me on my test.

Nicely explained.

BUt yet not helpful.

:|

very easy,thank u

Thanks, i feel slightly more confident towards my statistics GCSE

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 it..my 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?????

thanks!

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

HI martha. YOU CAN SEND FOR ME ASSIGMENT ABOUT STATISTIC, WHICH YOU QUESTION IN THÍ PAGE

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.?

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send answer for me: my email " tong_huyen_89@yahoo.com"

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

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

nice simple and very well presented

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

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?

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

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.

ThnX!!!

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!

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)

thnkz

wonderful thank you for helping me understand

very helpful

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

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

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

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

Thanks a lot Sonia...!

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

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

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..?

first!

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.

Great Job Sonia!!!

AWESOME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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

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

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

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

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

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!

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

thanks this helped a lot :)

THANK YOU.

Much easier than the formula my stat teacher provided.

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

http://www.ab126.com hong kong

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

really nice...thanks

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)

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

hello

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

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

It is very easy to understand.

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

THANK YOU SO MUCH,IT IS VERY EASY AFTER I READ THIS INFORMATIONS

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!!

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.

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

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

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

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

thankyou so much :D

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

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

excellent

thanks a lot sonia. very helpful

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

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

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!

Perfect thank you so much

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

THANKYOU!!!!!!!!!!!

you saved me from my maths test =))

Thanks for helping me finish my thesus.

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!

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

Good. Well done - that was short and simple.

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

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.

Thanks for your help,simple is always the best!

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

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,

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

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

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

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

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.

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

horrible

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!

great help better than the online instuctor

OMG - I no wat im going

THIS IS COMPLETELY WRONG, A PERFECT EXAMPLE OF WHY THE SOURCE OF YOUR INFORMATION IS SO IMPORTANT!!!!

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

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

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

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

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

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?

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

Hers the link to the website i built on this http://sapic.ath.cx/standard-deviation-calc

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

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

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

Thanks,You made my day

hi all,

Why i am getting 6.34 instead of 6.48

This is quite straight forward

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

Thanks man!

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

Much thanks !! very helpful.

hey thanks....it helped me a lot

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

Good thank u

It helped me a lot.

Whoever did this...u a genius in explanation

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

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

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.

There is an online tool to calculate std dev:

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

thanks lifesaver :)

So happy I found this!

Very easy to follow. thanks.

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

Thanks this was very useful

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

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

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...

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

very useful :) thanks

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?

So...what about significant figures?

very informative and useful thanks

Abbas Muneer Msc.Biostatistics 611-09 p.u

abbasmuneer611@yahoo.com

its help me a lot thanks

Abbas Muneer Msc.Biostatistics 611-09 P.U

abbasmuneer611@yahoo.com

abbasmuneer611@hotmail.com

its makes me easy thanks

Abbas Muneer Msc.Biostatistics 611-09 Punjab Univesity

abbasmuneer611@yahoo.com

abbasmuneer611@hotmail.com

thanks its so easy

Abbas Muneer Msc.Biostatistics 611-09 Punjab Univesity

abbasmuneer611@yahoo.com

abbasmuneer611@hotmail.com

very helpful =)

Get a life losers!!!

thanx for taking your time to help other in need.

thank you so much!!!

Well in, quite a good explanation!

u guys r so good

thank you

abbasmuneer611@yahoo.com

abbasmuneer611@hotmail.com

Abbas Muneer Msc.Biostatistics 611-09 Punjab University.

thank you

abbasmuneer611@yahoo.com

abbasmuneer611@hotmail.com

Abbas Muneer Msc.Biostatistics 611-09 Punjab University.

thanksssss! :)

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

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

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

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

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

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 :)

THIS HELP ME A LOT ON MY FINAL YEAR ESEARCH PROJECT.. THANKS..

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

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

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

tanx broder ....this was helpful

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

Thanks

Syed

Iqra University- Karachi Pakistan

thaaaaanks

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

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

Thanks a lot.

Thanks, helped a lot!

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

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

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

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

what does sd mean to the data?

it's Nice

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

than you so much

now i need ouation about t-test

kool example

very good and neat explination guys

Thanks! :)

huh i just started math and i cant understand

plz explain further

Thanks for putting this out there to help others.

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

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

Helped me a lot, thaaaaanks heaps!

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

thanks for posting this whoever u are. twas helpful.

Thanks so much for your help! :D

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

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

Thank You, this was very helpful.

mnm,,mn,mm

nmn,,nm,nn

I am doing a QM case and it has helped me

yeah!

what does the standard deviation actually find out

yeah what does standard deviation come out with DGOZZLE

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

Interesting, Thanx

YYYEEEAAAHHH!!!!!!!!!

HELP!

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?

I LOVE YOU THANKS

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

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

the comments on here are hillarious...

Ahhhhh this helped me!

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

not really its easy to understand

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

what the hell that wasn't my damn question

Just got some more points on my exam! thanks

Its a gra8 help to me. TXS

Very nice example, thanks

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

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

Sonia! Thank you...

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

It was simple yet helpful information. Thanks!

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,

Adham

JA WELL,THAX 4 HELPIN ME,BUT HEY THERE IS STILL SOME CONFUSION IN THIS,MAYBE SOMEBODY CAN TRY ANOTHER METHOD

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

Thanks. Helped out tons

omg thank you so much!! this is great!

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.

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!

that method is epic so cool

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

wow, lot of comments on here.

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

THANKS

it's very clear thank you sooo much!

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

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

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

I can my exam comfortably thank you Sonia

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!

That is exactly what I was looking for!!

Thanks a lot :)

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!

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

wow! awesome! you're AMAZING

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.

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!!

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

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

We have written a post on how Standard Deviation is applicable in Finance, especially when doing an analysis in Excel. Do check it out - http://www.edupristine.com/blog/what-is-standard-d...

Comments and feedback invited!

Interesting!!!

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 dabee_chiakua@hotmail.com

Thank you very much

omg its thugtastic yo

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

Thank you very much.

Thanks

thank u so so so so so so much

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

THANK YOU SO MUCH!!!!!!!!

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

SIMPLY EXCELLENT

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.

Thank you for this!

Helped me with applied science coursework!

THIS IE A PIE AND IT IS LIKE A LLAMA WHO EATS YOUR UNDERWEAR WHEN YOU ARE NOT LOOKING

In otherwords, this is EPIC POTATO :)

Stupid

No one will me read my comment;)

Thanks so much. Helping out my year 12 math.

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 :/

that was awesome.

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

Thanks

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...

Superb. Nice and easy to follow, thank you

very interesting and nice example thank u

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

thank you so much.it really helps me.

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

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

this was pretty good

mine is better :-) http://hubpages.com/education/deviation

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

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)

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.

Is 42 the variance in this case?

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

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.

awesome!!! you're the man!

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

Thank you, OMG

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

PLS CAN YOU ARRANGE EVERYTHING IN ROLLS AND COLUME,AND SHOW THE FORMULAR DETAIL?

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

cheers, very easy to understand

MIND WIDE OPEN!

GREAT JOB......

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))

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.

Thanks so much! that was easy to understand

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.

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?

The explanation was Awsm sonia :)

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

You rock Sonia! Great explanation!!!!!

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)?

Thanks so much for the explanation!

YEs i finally knows now

omg this is the best thing ever! THANK YOUUUUUU

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

This is perfectly explained, thanks a lot

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

agabrans, it is 14.2640

Thanks a lot saved me the test :D

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.

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!!

Its interesting wish it was explained with some graphics and more examples as it was explained on http://www.jpfis.com

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

thanks

1.

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.

very helpful. thanks.

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

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

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?

http://www.wolframalpha.com/input/?i=population+st...

http://www.had2know.com/academics/variance-standar...

or

http://www.calculatewhat.com/math/statistics/varia...

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.)

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:

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...

thanks fr the help

divide by n or n-1?

perfect explanation. thanks

Thanks to my virtual tutor, simplicity is the ultimate sophistication

¯\_(ツ)_/¯

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