Standard Deviation and Standard Error of the Mean

This video describes the differences between standard deviation and the standard error of the mean, and how they can be used to interpret data when the values are plotted as error bars on a graph.

[@his198]

Thank you very much for this video! I can't imagine a more clear explanation

[@PiersSupport]

Thanks Lena, I am glad you found it helpful!

[@deeplearning2552]

Kevin Piers what I don't understand is where does the number 6.33 at 4:18 come from? Standard deviation of a list of red-colored numbers (averages from 12 experiments with Jack, on 3:40), that is of [100, 101, 99, 114, 103, 101, 95, 99, 95, 105, 100, 93], is not 6.33 but 5.25. I've checked with Python with numpy, by hand, and using online SD calculators. All give population SD as 5.25 and sample SD as 5.48.

[@Tyokok]

same calc results. asking too.

[@KandMwedding]

it's because he has messed up a lot in this video. the s.d. of the first 5 trials listed for jack is 14.14 (not "16" as he claims later). and the SEM of *that* set is 6.32. so i assume that's what he was referring to with "6.33." ..as for the rest of the video, it's also not a very good explanation of a simple concept: i.e. that you can have quite variable data (say flipping a coin and calling heads "0" and tails "1") which could have a large s.d. no matter how many times you measure it (for the coin example it will approach 0.5 as the number of random flips grows), but nevertheless the uncertainty in the mean itself (represented by the SEM) will tend toward zero as you make more and more measurements, irrespective of how noisy those data are. the video could've used a better example (for instance, a person running anywhere is not a good example of independent data, as there could be trends in either direction -- faster or slower -- depending on the time between trials; thus these data are not even appropriately lumped together like this) and as you point out, he could've at least double checked his math before posting.

[@winvictorywin5612]

Piers Support Hello sir, I am having airborne dust concentrations data as PM10, PM2.5, PM 1 . These data was taken before and during dust producing work in a civil construction site. N=5 How can i compare these before and during operations data ? It seems that there is percent variation in dust concentrations in atmosphere between before and during operation data based on particle size. Before operation: PM 10 ( particle size less than 10 microns) is sharing 40% of total airborne dust, and PM 2.5 ( particle size less than 2. 5 micron) shares 10% of total airborne dust. During machine operation: PM 10 shares 60% and PM 2.5 10% only. It seems that PM 10 share is increased due to that machine operation? Which test is suitable for analysing these type similar data for discussion ? How to use statistics? Any comparison among these particle sizes? thank u.

[@davidrosen5137]

Four semesters of graduate level statistics, and you accomplished in 10 minutes what four different profs failed to accomplish at all. Thank you!

[@katomoon6170]

No better explanation than this one. Can't thank you enough Dr. Piers. You're an exceptional instructor with the ability to clearly, precisely and simply explain very complex statistics topics. God bless you. Much appreciation from Uganda - East Africa.

[@quintonwilson8565]

This is thee single best video on this subject on YT, thank you Dr. Piers.

[@vikkirossiter]

I'm doing a stats class now and I understand more from this 10 minutes than the whole lecture on it. Much thanks

[@SmokeyHooder]

Watched this three times and finally I understood this. The best explanation I have found on this topic, no doubt!

[@futurefee1444]

Excellent breakdown, thank you for your service.

[@emmayu1847]

This is the best statistics video I have seen. Such clear explanation and great presentation. Thank you!

[@soknya]

I need to watch it twice to confirm my understanding. Thank you for a clear explanation

[@jessicafb5398]

Thank you for explaining this concept so clearly and with great humor. Very helpful and enjoyable!

[@akshu251]

Sad that I watched it too late. But as it is said, better late than never. Amazing video. Now, I will never forget the difference. Thank you.

[@912sonic]

I'm glad I found this too. Better late then never honestly

[@wilsonvuong8855]

This is without a doubt the clearest video on SEM. Thank you so much for your efforts.

[@NiekVink]

agree!

[@neerajrokaya1132]

subscribed just after seeing this video..cant explain how aewsome this explanation is

[@jamesrobertson9149]

This is a brilliant video because it makes clear what the SEM is. first class! thanks.

[@aziziqbal2777]

Most clear explanation on this topic I have seen on youtube. You've earned yourself a subscriber.

[@genevieveperdue8019]

Thank you so much, this is a wonderful tutorial. I am a TA for a data analysis course and was having the hardest time figuring out how to emphasize the difference between SD and SEM. You did it very clearly and simply!! You just saved my students from a very confusing lab explanation :)

[@PiersSupport]

Thanks for the positive comment Genevieve! I'm glad you found it helpful.

[@cajogos]

Really good refresher to these statistics ideas, I had completely forgotten what standard deviation and SEM was! Thanks a lot!

[@p_mouse8676]

I always explain it this way to students. SD is a measure of how big the spread is between samples. SEM is a measure how exact we know the average (or mean). It starts to get interesting when SD is relatively big. At that point one could argue how valid the test actually was. Because it's perfectly possible that the SD is very big (individual samples are widely spread) but SEM is quite small at the same time.

[@user-pv5lg7hr1w]

You are a very good teacher and that is very rare nowadays.

[@chitritaghosh4279]

Thank you very much for the video. I am a medical student. I needed a understanding of the difference between SD & SEM for community medicine. Your video helped me a lot...

[@michellexhg6077]

finally the video that answered all my questions! good job and thank you 💪🏼

[@dr.renupoonia5337]

very simple but effective way to teach these two terms and their use. Thanks a lot.

[@sarahbronte3043]

that's is really a simple access to the two complex concepts, thanks, that's really helpful for the psychology student without a math background to understand. you really knows what we are confusing in each steps.

[@devong4722]

You have a gift. Needed to brush up on a few of these for a class and this was concise yet coherent. Thank you so much!

[@ramzyhedia1277]

Thank you very much for taking the time and effort to prepare this is a really very interesting and useful video. God bless you

[@josephinetityiwe4434]

Thank you very much for enhancing my understanding of SD and SEM.

[@cbrewster10390]

THANK YOU. I have consulted 10+ sources trying to figure out the difference and was beginning to feel like a complete idiot until you.

[@ayabulelamkutswana2110]

watching this and I have a submission in two days, really helped thank you Doc!

[@cindybokish1534]

Thank you! Appreciate you taking time to explain. I cannot say how much this helped me.

[@miladiouss]

You create intuition, something that other videos don't.

[@andrewlukkuz369]

Thank you for making this video, I have a chem quiz on this and for some reason I couldn't wrap my head around the subject, your video helps alot bro.

[@dinglixi5179]

This solves my question which bothers me for so long. Thank you so much!

[@manikant1990]

Excellently explained, please make more videos of these sort in statistics and any other topic. :) Great job again!!

[@lensmaticoptical4083]

Thank You Sir. It is a best explanation ever i have seen on this topic. Amazing... God bless you.

[@NiekVink]

Finally a clear video on SEM, this helped a lot. Thanks!

[@subramaniank6360]

Clear explanation of standard error mean

[@prakash_kp3039]

Thats a great , concise and holistic video.

[@JaqulinePrabu76]

Unreasonably good...great presentation!!

[@jonelabutyte6617]

very good and quick refresher of SD and SEM evaluations❤ Thank you!!!

[@okiwahboris1597]

Thanks for the video, i really understood much today, and i am defending my DVM tomorrow. God bless you

[@THE______TRUTH]

idk why but I laughed at the example of examining the data of Jack and jill who ran up the hill.

[@troberson5501]

Thank you for explaining the significance of SD and SEM as it relates to data interpretation. I had plenty of definitions and calculations but no explanation, until now, about what those concepts are telling me about the data I'm looking at.

[@KajiAwaley]

Yes data interpretation is more helpful from this video. Thank u Kevin

[@luisborgesjr]

This man really knows his stuff!

[@belal7490]

Thanks very much Dr. Pier for your efforts. This is a very useful video.

[@amosbako3981]

Thank you for this video, it's a must-watch for statistic student

[@Selorm4christ]

Thanks very much. This info is statistically a life challenger.

[@logjonbudha137]

This video is most important for the understand of S.D.& S.E .Thnku so mush sir!!

[@dreamliner707]

That explanation was so clear. Thank you.

[@aceplusplusplus7652]

Thank you Dr Piers!

[@user-uh9gg5dc5k]

GRACIAS!!!! Well done! Clearly and cleverly stated.:)

[@movement9192]

Excellent explanations of sd and adm

[@yaswanthbangaru9116]

An Incredible way to put it!

[@MDMAx]

Thank you for the clear explanation!

[@argytzak]

I used R to calculate the standard deviation of the averages and got 5.484828 (instead of 6.33 that you show). Note that the sd() function is R uses denominator n - 1. Why the difference?

[@mohammedalqahtani2643]

Truly you made it so simple and easy, Thanks!

[@dheerajvarapana1124]

Fantastic explanation. Thanks a lot for your time and help.

[@RobvanMechelen]

Excellent explanation! my compliments. However when you mentioned Jacks 12 trials, The Mean of the 12 means = 100.20 and SD = 5.48. The SEM = SD/ sqrt(12) = 1.58, whereas you mention 6.33

[@matthewx2105]

That's ture, my final result is 5.48 as well. I'm quite confused about 6.33...

[@Alex-fk3ni]

"The Mean of the 12 means = 100.20" - where did you get this number? The mean of 12 means is 100.42

[@zhongdasun8772]

the SEM is just the calculation of the STD of the mean of that 12 numbers, which means you do not have to /sqrt12. so the SEM is 5.48 as Mattew mentioned below.

[@zhongdasun8772]

@@matthewx2105you are correct

[@RobvanMechelen]

@@zhongdasun8772 Thanks

[@Mamatin2]

This was so great! Thank you, Dr. Pierce!

[@ozgekrklk4718]

he is explaining very well , thank you

[@rebekahcook9487]

Super helpful video and very well presented. I just needed an overview and Jack and Jill were a helpful way to do it. And thanks for the coffee bag image ... that totally distracted me ... in a good way!

[@PiersSupport]

Thanks for the feedback Rebekah - glad you liked it (and the coffee :)

[@harikishanbusa4714]

Best explanation! much thanks.

[@rebeccagoldin756]

There is a slight error in your interpretation of the 95% confidence interval. You say that the error bar contains an interval that, if you were to repeat your experiment 100 times, would contain the average 95 of 100 times. Instead the confidence interval (indicated by the error bars) changes each time you repeat your experiment. The correct statement is that in 95 out of 100 times, the calculated error bars will contain the “true mean.” This is true for both SEM and for SD. Otherwise, a truly excellent explanation with great graphics!

[@PiersSupport]

Thanks for the clarification Rebecca!

[@VaibhavYawalkar]

best video on this topic. Thanks a lot sir.

[@brookesullivan6663]

This was such a helpful video thank u so much

[@minutetolearnit8449]

You are a legend sir 🙏

[@adatse51849]

Very informative and perfectly explained!

[@nicholaskatto]

thank you professor God bless you

[@oliverbird8320]

You explained so well on the concept!!!!!!!!!!

[@pig_samurai]

You are my angel~ Mr. Kevin thank you!

[@SaberNezumi]

A really good explanation. Thanks for the video.

[@xuul7338]

Great video! Thanks for sharing, this was clear and concise.

[@mateom6596]

what a lucid explanation. thank you.

[@nandiniB11]

Excellent explanation

[@itssmsn91]

Thanks for the video with such a nice explanation :)

[@anirudhsood2006]

Thank you so much for the video.

[@noazamstein]

Awesome video! so clear and concise

[@ritachaudhary5780]

Thank you! Well explained

[@altafalinaushad6368]

SANTA MARIA!!! You saved my life!

[@longjamboris1041]

very helpful video. thanks again

[@lesliehermann7267]

That was SO helpful! Thank you!

[@A_Box]

Hello. I was attempting to double check your work at 4:22 and I happen to find different results. Using Excel, the sample standard deviation for the set of averages is 5.483 and the population sample deviation is 5.250. Is this indeed a mistake or am I missing something?

[@TonyTorzido]

I came here for STAT 300. Now I'm back for Ecology lol. Thanks, Sir Piers!

[@MrEndocytosis]

Nice video thanks! Would you say in general that when a single person does the same test repeated times (person running a mile 5 times) you should show SEM but when you have a group of people that do the same test such as a team running a mile, then you show the SD?

[@ansariarbaz3374]

Just superb❤️❤️🔥🔥

[@lllMrKrobylll]

Very nice and clear video. Thanks a lot!

[@disha3558]

I would have topped in maths if I had found you sooner. 😅

[@benlee3545]

Hi Kelvin, are you able to show how you calculate SEM=6.33? I tried to compute but my answer is about 5.5.

[@PiersSupport]

HI Ben. By golly it appears you are right. I put the values into the spreadsheet and got 5.48. Thanks for picking this up and sorry for any confusion!

[@benlee3545]

Thank you very much. This video is really friendly even for beginner who knows nothing. You really know understand the beginner difficulty. Thumbs up for you. :]

[@danielpavon9623]

THANK GOD SOMEONE ASKED THIS, I was going crazy. I too copied the averages of those 12 trials into Excel, calculated STDEV.S and got 5.48.

[@baransakallioglu]

In calculations, everything seems to be rounded. For example 5:15 actual stdev is 15.81 but rounded up to 16. 16 / sqrt(5) = 7.155417527999327 and rounded up to 7.16 etc.

[@jeranrai3488]

please help me, really dont know how and where to take in the class for Applied Data Science Module that i was accepted from, when i login the worldquant university portal than it only prompts for the Master degree registration

[@dzb33]

I know Dr. Piers says he doesn't care about how we know that 95% of the probability lies within 2 SDs of the mean in a normal distribution, but it's actually really simple. Take an integral from -2 SD to 2 SD of a normal (or Gaussian) distribution. Anyone who's worked with probability distribution functions should be familiar with doing things like this, since you integrate the probability distribution function to calculate probabilities (indeed that's what we're doing here) or cumulative distribution functions.

[@ph3124wr]

Many thanks, Dr. Pierce. I have learned a lot. I hope I can give you two thumb-ups.

[@joshbridges4719]

Thanks for the video. It was extremely helpful! My only question concerns the interpretation of the two graphs at the end of the video where they either completely overlap or don't overlap at all. You stated this means there is either no difference between the two populations or there is a difference. Could you clarify this point? Does it suggest that (in the first graph), it doesn't make a difference whether you watch the videos or not whereas with the last graph, there is an impact, on say, a student's grade?

[@PiersSupport]

That is certainly a good summary of the graphs as far as I understand it. There are probably more nuanced interpretations, but that is a good working model. Cheers.

[@joshbridges4719]

Kevin Piers Thank you for your response. It helps clear up some things.

[@Ferenczi69Aron]

I appreciate the simplicity of the explanation, but how is it that when I calculate stdev of the averages in red (from 3:50) using Excel's function STDEV.S, I get 5.48 and not 6.33?

[@sexyaki704]

Ferenczi69Aron try STDEV.P

[@hyacyn_th]

this guy is amazing

[@ZhigaZhega]

Thanks man, most helpfull explanaton on you YT.

[@gehuishen5415]

Very clear explanation!

[@benstolman4073]

Best video out there

[@taladiv3415]

Nicely clear explanation of the two concepts. Keep up the good work :)

[@quanzhaohe1221]

Very clear explanation! Thank you!

[@cicinindivin3689]

±2 SE is 95% only for infinite measurements, if not is ± t student (2 tails) for n-1 observations/items