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# Standard Deviation - Explained and Visualized

More From: Jeremy Jones
5211 ratings | 801988 views
Video transcript: "Have we discovered a new particle in physics? Is a manufacturing process out of control? What percentage of men are taller than Lebron James? How about taller than Yao Ming? All of these questions can be answered using the concept of standard deviation. For any set of data, the mean and standard deviation can be calculated. For example, five people may have the following amounts of money in their wallets: 21, 50, 62, 85, and 90. The mean is \$61.60 and the standard deviation is \$28.01. How much does the data vary from the average? Standard deviation is a measure of spread, that is, how spread out a set of data is. A low standard deviation tells us that the data is closely clustered around the mean (or average), while a high standard deviation indicates that the data is dispersed over a wider range of values. It is used when the distribution of data is approximately normal, resembling a bell curve. Standard deviation is commonly used to understand whether a specific data point is “standard” and expected or unusual and unexpected. Standard deviation is represented by the lowercase greek letter sigma. A data point’s distance from the mean can be measured by the number of standard deviations that it is above or below the mean. A data point that is beyond a certain number of standard deviations from the mean represents an outcome that is significantly above or below the average. This can be used to determine whether a result is statistically significant or part of expected variation, such as whether a bottle with an extra ounce of soda is to be expected or warrants further investigation into the production line. The 68-95-99.7 rule tells us that about 68% of the data fall within one standard deviation of the mean. About 95% of data fall within two standard deviations of the mean. And about 99.7% of data fall within 3 standard deviations of the mean. The average height of an American adult male is 5’10, with a standard deviation of 3 inches. Using the 68-95-99.7 rule, this means that 68% of American men are 5’10 plus or minus 3 inches, 95% of American men are 5’10 plus or minus 6 inches, and 99.7% of American men are 5’10 plus or minus 9 inches. So, this means only about .3% of American men deviate more than 9 inches from the average, with .15% taller than 6’7 and .15% shorter than 5’1. This reasoning suggests that Lebron James is 1 in 2500 and Yao Ming is 1 in 450 million. In particle physics, scientists have what are called 5-sigma results, results that are five standard deviations above or below the mean. A result that varies this much can signify a discovery as it has only a 1 in 3.5 million chance that it is due to random fluctuation. In summary, standard deviation is a measure of spread. Along with the mean, the standard deviation allows us to determine whether a value is statistically significant or part of expected variation."
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so mean is useful in finding the cross-subsidization of money...
Cyrious (16 days ago)
sees 467 dislikes and clicks off QUICK!!!
Cyrious (16 days ago)
ok came back to watch and it was not that bad
Windex from the 1990s (29 days ago)
I don't understand where the .15% come from
Jaison Jacob (1 month ago)
God bless you sir...
Where is chef john???😅 I have food wishes that arent being met!!!😉
Henry Smith (1 month ago)
I understand why some think this video is stupid and why others think it's great. Does the video touch on all points and does it demand data without reference? Yes, I would say it's informative but poorly made.
Uzair Hameed (1 month ago)
Best explanation I've found. <3 Ignore haters
Cali Steve (1 month ago)
Hello this is chef john from foodwishes withhhhh.....Green Chile PestoOOoooo
Anthony Turcios (1 month ago)
8 weeks in tom 3020, stats for business, and this 3:42 vid explained the concept so much more clear and concise
Tina Krell (1 month ago)
Thank you very much for the explanation. One question on min 2:29, if 5'10 is our average and "base" and the standard deviation is 3 inches. You write that the spread is 5'1 - 5'4 - 5'7 -5'10 (average) - 6'1 - 6'4 - 6'7 inches. Shouldn't it be 4'20 - 4'50 - 4'80 - 5'10 (average) - 5'40 - 5'70 - 6'0 inches? Thanks in advance.
Ambalavanan T (1 month ago)
No matter wherever I go . Lebron James comes there..
Bill Miller (2 months ago)
The song sounded like the RLM Half in the bag intro
Nicola McBain (2 months ago)
But the Formula... Duuude XD
NOU GAMES (2 months ago)
I love how he DOESN"T fucking explain how he got \$28.01 at 0:34
Laura Payne (2 months ago)
Thanks for the great PowToon! Really great production quality. I'm not an expert on SD, thus I consulted your video. I love seeing experts in their filed find ways to communicate difficult concepts in concise and meaningful ways! Well done! (And adding a transcript - A+)
Manit Rotan (2 months ago)
inches?? what the fuck....lol k bye
Latoya Derrick (2 months ago)
literally better than my shithead professor
Pete 1 (2 months ago)
That's a really good explanation of this. Thanks.
Allena May (2 months ago)
to Wood'N" Stuff...I agree totally. I thought I was the only one confused....ugh....but the video definitely made it worse. I wanted him to explain also where he got the standard deviation of \$28.01....oh well
Y...you didn’t explain what standard deviation was?
Wer’e?
M A (3 months ago)
sigma balls
GuacamoleKun (3 months ago)
OKAY, so because I am not a math person, tell me if this is a correct assumption about how I should feel when I hear something is X standard deviation. 1 SD: worth noting, but fairly normal. 2 SD: somewhat remarkable. 3 SD: DAMN son, look at that! Anything more: An actually really crazy number, very unique.
Aslan Delroba (3 months ago)
What’s that song in the intro?
Atiharsh Singh (3 months ago)
Awesome explanation and super sexy voice.. what a delight TBH!
Airdrop Applier (3 months ago)
please help understand how you found the value for lebron being 1 in 2500 and Yao ming 1 in 450 mil!
James Bennett (3 months ago)
good video
This mafs ain’t that quick
5ben2 (4 months ago)
Sigma balls
jasper cheng (4 months ago)
but yao ming's chinese
Caleb Strohl (4 months ago)
Chef John? Oh nvm.
Curtis Franz (4 months ago)
I"ve been struggling with this concept. Not anymore. Thank you!!!
Syed Aqeel Bukhari (4 months ago)
Jeremy You won my Heart
Vidhya Rajan (4 months ago)
never heard a better explanation
Canary Labs, Inc. (4 months ago)
Abhiroop Bhattasali (4 months ago)
WOWWWWW..... Thank You... I always knew what it is, never saw it, and i really really wanted to see it. Now I can...
Diego Reyes (5 months ago)
Confusing
Alden22 (5 months ago)
Hello can you please elaborate the relation of the \$28.91 std deviation to the set of data.
profealexandrasierra (6 months ago)
Super good! I love it! Thanks
clewis5039 (6 months ago)
Thank you for the transcript, Jeremy, and for taking your time to present this information. Very much appreciated!
Porry Napa (6 months ago)
Thank you, I've been finding the meaning of the standard deviation. I understood it better now! :)
EricDySart (6 months ago)
I have to agree with the comment below me. This is NOT how you teach something so that people can comprehend it. There's an assumption within the video that the viewer comprehends the jargon used in this video. Why is it that people who want to teach this, revert to jargon to explain it. more confusing then helpful for sure.
yk2015 (6 months ago)
Bruh im in year 9 learnin this and now my brain hurts
Bamlak Bahiru (6 months ago)
fuk are u talkin bout
que
Bamlak Bahiru (6 months ago)
you son of a donkey butthole
Bamlak Bahiru (6 months ago)
yeah funny looking
Bamlak Bahiru (6 months ago)
Thanks man I appreciate it
Bamlak Bahiru (6 months ago)
wow you're very funny
Zeeshan Waheed (7 months ago)
what conclusion can be drawn from an experiment in which average deviation is very small ?
Zeeshan Waheed (6 months ago)
Bamlak Bahiru i am doing phd in relativity
Bamlak Bahiru (6 months ago)
what are u a techer ?
Perhaps this video is not made for level of iq or he's explaining this for people well acquainted with statistics, in other words im more confused after this video
Varuna (7 months ago)
Too much jargon in the explanation. Still completely lost. Waste of time.
Russell Boyles (7 months ago)
Thanks!!!!!!!
Fought lasts (7 months ago)
I am having a problem. The data that I’m collecting is about money and when I get the 1,2and 3 standard deviation that resulted that I get is minis. But money can’t be minis!! Help plz.
Kris (7 months ago)
Hi! May I ask, how would I know if my data are STATISTICALLY SIGNIFICANT or EXPECTED VARIATION? and what does it mean?
Kris (6 months ago)
That's the problem. They won't answer. :'(
Bamlak Bahiru (6 months ago)
Maria Charra (8 months ago)
What????
Lucas Nascimento (8 months ago)
Pax Torumin (8 months ago)
Yes, but how do you _calculate_ a standard deviation?
Jeremy Jones (8 months ago)
Pax Torumin Awesome! I’d recommend using a calculator (online, google sheets, Microsoft excel, or graphing calculator) if you have to do a lot of calculations. :)
Pax Torumin (8 months ago)
Huzzah! Thank you! I'm working creating a tabletop RPG for some friends of mine and the core mechanic uses dice pools with all kinds of different dice. Being able to calculate a standard deviation will be super helpful in balancing all the math.
Jeremy Jones (8 months ago)
This video is more of a conceptual introduction. Here's a video showing the calculation: https://www.youtube.com/watch?v=WVx3MYd-Q9w
Drew Arnold (8 months ago)
If you're complaining about the quality of this video in any fashion, then you desperately need a cold cocktail on a mild and sunny day on a tropical beach likely no more than 1.5x standard deviations from where you are right now as you read this silly comment. If you're not complaining about this video, I wish you the same. This video's producer made YouTube just a little bit better by adding it.
Airdrop Applier (3 months ago)
please help understand how you found the value for lebron being 1 in 2500 and Yao ming 1 in 450 mil!
Jeremy Jones (8 months ago)
Drew Arnold Hahaha amazing! Thanks for this! Glad you liked the video.
carly keeney (8 months ago)
Loved this!! made complete sense- i suggest those that are confused watch his video in standard deviation calculation first than watch this.. this is like a part B to a Part A.
Brandom Herrera (8 months ago)
11/10 perro y +1000000000
Asriel Fox (8 months ago)
who else is watching this from mr.crabtrees
Meundies (8 months ago)
I don't understand how you got the static 1 in 2,500
Rohail Nasir (10 months ago)
Such a clear explanation
Cesar Diez (10 months ago)
good fucking video, explained very well
K1dPhresh1 (10 months ago)
Finally, I get it!!!  And can regurgitate it, which is very important.
qaqsqw (11 months ago)
You sound like Napolean Dynamite's brother.
Jeremy Jones (11 months ago)
Chacko Jegan (11 months ago)
Finally! Thank you so mucch
Raghava Bhat (11 months ago)
Unlike equations, this is way easy to understand what is standard deviation
Howard Koor (11 months ago)
Well done:))
Wilderness Truths (1 year ago)
Huh what the fuck are you talking about for one you going so damn fast my brain can't even wrap my head around what you just said to even try to understand it before you jumped on something else and now I'm confused slow the fuck down people are stupid
Ashish Jha (1 year ago)
Best explanation of Standard Deviation, I have ever come across
Rachelle Leveille (1 year ago)
I use pow toons too
I I (1 year ago)
After searching google for a half hour and dealing with people who couldn’t explain anything to someone who doesn’t know math, this video gave me the straightforward answer I needed. Thank you for actually providing information rather than trying to seem smart by making the explanation more complex than necessary.
John Kneen (1 year ago)
Thank you this was so helpful
Phantom Lancer (1 year ago)
Fuck statistics
Mikayla Bowman (1 year ago)
Jack Vial (1 year ago)
Good explanation
gtfffv (1 year ago)
So Yao Ming would be statistically significant?
inactive youtuber yep (1 year ago)
Thank you so much
Malek Agha (1 year ago)
Thanks a ton, was confused so much on this but your video cleared everything up :)
At 02:15 how did you determine the + or - 3"?
mohana pandian Raju (10 months ago)
It is understood that a "bell curve" naturally happens in most data used in the world. Process variation is defined as "sigma". There are 6 process variations (3 on the left from the mean and 3 on the right from the mean). The separation is due to how the "bell" curve or the sample behavior changes drastically at these points (inside these specific ranges). Sorry for not being eloquent.
R S (1 year ago)
didnt do an example fuck you
Shivangi Singh (1 year ago)
Nobody ever told me WHY must standard deviation be calculated in the first place. Thanks for explaining it so well !!
Shivangi Singh (1 year ago)
Nobody told me WHY must standard deviation be calculated in the first place. Thanks for explaining it so well !!
hannah edits (1 year ago)
Thanks
mosbo004 (1 year ago)
This has made a BIG difference in helping me understand this topic..THANK YOU!!!
Sett Naing (1 year ago)
Thank you so MUCH!!!!!
2583060 (1 year ago)
sounds like he is saying Meme instead of mean
Ashok Raju (1 year ago)
thank you for explaining clearly.. nice one!!
Tim Duggan (1 year ago)
This video actually does at no point explain how to calculate sigma/standard deviation.
Dylan Beauchamp (1 year ago)
Whats popping mrs benz math class
Ryan Buzon (1 year ago)
thankyou so much:)
limelight_sam (1 year ago)
WOW! I got the key concept ^_^
salohciN D (1 year ago)
I hated statistics class. Turned out to be the most useful thing i learned in college
Hennah Saber (1 year ago)
Great explanation, thank you!
Hottea G (1 year ago)
confusing
Subrahmanyam Sanka (1 year ago)
great explanation!!
rony kurian (1 year ago)
Best explanation
Mudit Singh (1 year ago)
wow.....Thanks for making this video.
Ellen Graybill (1 year ago)
Thank you for the clear explanation.
Devanshi Jansari (1 year ago)
You have explained it in a very simple way which i was not expecting to be available at youtube... Thank you so much and keep making videos like this... It would be appritiable
Debarshi Majumdar (1 year ago)
standard deviation can be used as a measure of dispersion for any data-set... that may or may-not come from a random variable which follows a probability distribution such as a normal distribution. however, the concept becomes 'useful' (in calculation of probabilities or frequencies) if the distribution of the variable is known. especially useful when the distribution is symmetric - as in the case of a Normal distribution.
Football Videoz (1 year ago)