Standard error of the mean | Inferential statistics | Probability and Statistics | Khan Academy
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- Опубликовано: 4 окт 2024
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Standard Error of the Mean (a.k.a. the standard deviation of the sampling distribution of the sample mean!)
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i've done a PhD in maths and I STILL come back to the Khan videos to refresh my basic stats. true story. what a dude.
R u for real?
Amarpratap singh when u have a phd your brain capacity fills up really fast and u tend to forget older stuff
@@ohmingfeng9351 So true. I have had 3 statistics classes and now taking my 4th. My last class was 9 years ago. I am back here to review while I work on my graduate degree.
oh thank god. I'm not alone. I've taken 4 advanced modeling and stat classes in grad school now and I still need to keep refreshing.
Good for you doctor :D
Just in case people are having problem with some of the definitions which I have been looking for the past hour.
sample mean == you take a sample of n data and finds the average.
SAMPLING distribution of sample mean == basically do the sample of n data repeatedly many times, so you get many means, and use those means as your distribution, in another words, you get a normal distribution full of means, even the extreme numbers are one of the means.
σ = population standard deviation.
σ (with subs x bar) = standard deviation of the 'SAMPLING distribution' of the 'SAMPLE means'
s = sample standard deviation.
Hope it helps for those of you are still confusing with the naming conventions.
and of course, n is always referring to sample size (numbers of x), not the sampling size(numbers of x bar)
He's the messiah
@@s2productions242 mans the long lost saviour we been searching for
@@eliizabeth7557 could you please say what will be the formula for standard error when we take just a single sample, hence just one mean.
Will it be
S.E = S.D of sample/sqrt(n)
Like basically S.D of sample instead of population.
thank you so much God bless you
My brain is gonna explode
Mine is already exploded.
Same here :(
You reduce my anxiety
@@solo-lt8ez happy to help
HSHAHAHA
I have a midterm tomorrow ,started the day without knowing a thing and now I can even solve questions. I wish my lecturer were you, every person deserve quality education thanks Sal
me also
I love how he explains everything using common sense! makes you able to visualize things easier therefore understanding things faster! Teachers nowadays just read equations off slides..they are useless might as well read equations from a textbook.
13-14 years later and I've gone through school for as many years as this comment has been up. In my second year of university right now. Totally true.
clear as mud
best voice, best personality, best teaching. I grew up watching u and here i am back again for my medical licensing exam (USMLE Step 2 CK) to study epidemiology with you. I love u so much. Thank u for everything!
Just gotta say, I really enjoy the videos. Thank you Mr. Khan.
Needed to revise this while studying biostats in my MBBS....came back to the legend.... Jazakallah
Your approach of emphasizing a firm grasp of the CONCEPT - which is helped tremendously by your illustrations, examples and "friendly" narrative - before going to complex mathematical formulas (proofs) is an excellent one!
I look forward to seeing more. (Hope you get into ANOVA).
Many thanks for making this help available.
"You know, sometimes this can get confusing because you are taking samples of averages
based on samples. So when someone says sample size, you're like, is sample size the number of times i took averages or the number of things I'm taking averages of each time?
....
Normally when they talk about sample size they're talking about n..."
My goodness this was so clarifying My book doesn't really make this distinction clear or apparent, so it's always a guessing game to try and figure out what they mean by sample size, at least for me. But now it's clear. Thanks, Sal! Saving the day once again.
"let me use a different colour for that"
-khan academy (the greatest teacher ever)
This video and his explanation is so clear and straightforward! If you watch all the videos before this and understand all of those concepts, you should be able to understand this easily. Great job; thank you
OMG! I never knew the formula. But I guessed it correctly before he revealed it. Amazing. I wonder if it is his way of teaching that instills the concepts into our brain so quickly.
I swear, in half of the videos regarding this issue, they say that σ reffers to the the sd of the sample and the other half say that σ reffers to the whole population. They mess so badly with what each parameter in the SE=σ/√n formula stands for.
So clear about it
15 mins can explain everything about this topic
the professor in the university has spent lectures to explain nth
This guy is a champion in optimizing any topic 🙌
♥️Love from India🇮🇳
I have a statistic exam this Friday. Studied Japanese and now communication, but statistics is lodged in my curriculum for some weird and torturing reason. I still think I'm doomed, but I'm less doomed thanks to you guys. Greets from Belgium
Standard deviation of the mean is a parameter describing the distribution of all sample means of a a given sample size n from a population.
standard deviation of the mean = (pop. stdev)/sqrt(n)
Standard error of the mean is an approximation of this value calculated from a single sample.
standard error of the mean = (sample stdev)/sqrt(n)
I really really appreciate the way he teaches... so nice and practical. I was never been able to get these concepts but now its crystal clear . can I please know the educator's name?
Thanks so much for taking the time to make clear what you're talking about. I've left two linkedin stats courses unfinished because both times it got to the point where I just couldn't keep all the Greek letters straight nor could I always tell whether the instructor was talking about a sample, the population or a sample distribution. Thanks!
to compare how precise is your sample data compare to your population data. if the standard error is large, that means your sample data is not a good representative data for the population, vice versa, if its small, it means the sample data is representative! hope that helps :)
I swear my stats class would be so much better if the crappy professor just played up Khan Academy. Fantastic organization totally deserve every dollar they get
So helpful! Thank you so much for doing this!
When I think of sample size, it means the number of observations per sample, hence the lowercase n.
For example, if one sample is 1, 2, 3, 5, and 9, those are 5 observations, so the sample size is 5. Another way of looking at a sample is by thinking of it as a data set, and each individual observation is a data item. If you call the entire thing a sample and everything in it a sample also, it gets really confusing especially when you're trying to get your mind around the concept of the sampling distribution of the sample mean.
Anyways, your videos are the only reason that I'm passing my business stat course, thank you so much!
You wrote, "If you call the entire thing a sample and everything in it a sample also, it gets really confusing especially when you're trying to get your mind around the concept of the sampling distribution of the sample mean".
I cannot agree more strongly. This is a VERY common and totally avoidable error made in almost all of the online presentations by statistical evangelists.
@@jamesleem.d.7442 Can you please say what will be the formula of standard error if we are working with a single sample of maybe 30 observations.
Will it be
S.E= S.D of the sample of 30 observations/ sqrt(n=30)
Basically if we are working with just one sample we won't have standard deviation of sampling distribution of sample means, right?
This video muddles the distinction between "standard deviation of the mean" and "standard error of the mean".
he describes the "standard error of the mean" as the "standard deviation of the sampling distribution of the sample mean", which is what it actually is. And he does make the distinction between this and the "standard deviation of the mean". The word "standard deviation" is usually not used when describing the "standard error of the mean", however it's useful to understand how the operation to get to the "standard error of the mean" is related to the operation to get to the "standard deviation". It is really just inception of variance.
Thinking of standard error as a standard deviation of sampling distribution is so simplifying. Thank you for this.
Super video. Good to see how much clearer the potentially confusing notion of standard error of the mean is. Thanks a lot for making it clear and exciting.
school time = 6 months
khan time = approx. 15 min
knowledge acquired = SAME SHIT
hey buddy you wrote this 6 year ago . How are you right now? How's is Life ?
It makes me feel so much better that people are coming back to review, I don't know, AP math?
This sent shivers of my stats classes.
Simulation made it clear. I was so confused before that.
finally talks about standard error of sample mean at 7:30ish
!!!!
you just save me about 7 and half mins
its easy :
n:= number of samples to compute the mean
sigma:= true variance of the original distribution.
sigma_x:= variance of the means ( computed from the n samples ), the square root is called standard error
basic message of the video := sigma_x = sigma/n . Variance of sample means can be approximated with the true variance and the number of samples we take.
However, I think the formula is more usefull the other way round, since most time people don't know the true variance :
sigma_x*n=sigma
Thank you, thank you, thank you, this was actually very very helpful.
I have my exam tomm. and i felt this as the most reliable source...May God bless you :)
Thank you very much for all you videos. It really helps me out in my statistic courses!
Great! I finally understand medical stats!
6:32 "I'm just making that number up." ...No problem, I do that all the time. =p
When your airhead professor goes over an entire chapter in 20 minutes, writing some ambiguous notations on the board, expecting everyone to understand his chicken scratch.... you go to Khan Academy. Thank you for actually TEACHING!!!
what I find confusing is the word "sample" - when you say "sample" in English - do you mean one observation or do you mean an action where you take (e.g. randomly) several observations which, together, build one sample?
now find his wording is confusing in statistics he is pretty good with many things for example calculus , but I realised that he is not perfect. people has to be objective.
I find you speak incredibly fast, if you could slow down this video would be perfect. Im in stats know learning the standard error and I found it helpful but like I said its too quick so its hard to follow.
Thank you though for the video!!
Would the distribution become a vertical straight line when n -> infinity? Since the standard deviation -> 0
But how come you said the curve become perfect normal when n-> infinity?
When n = size of population (from which samples are taken) the distribution will be a straight line/peak. He is incorrect, when n approaches the size of population, the standard error becomes 0.
N can't be infinity. N can only increase up to the population size.
Your videos are really very very helpful for me , please if u have do some video regarding complex,differential and calculus icant able to understand it clearly
You bring the formulae so close home by making them so logical. Thanks for all your efforts :)
Thank you so much! Explained very beautifully! 👌🏼👌🏼
So if I understand everything correctly, you can only estimate the standard error if you are performing multiple sampling, e.g. asking 100 people (always other ones), 100 times about, say, how long they have slept last night. Is it possible to estimate standard error using only one trial/measurement ? Or in that situation, the only thing we can obtain is the standard deviation ? So one would expect values like mean+-SEM to be more typical for population studies, gene expression analyses of numerous group of patients, but not in a single gene expression analysis where you compare, say, 5 control samples vs. 5 experimental samples ?
Hey why so many "its too confusing" comments, watch his previous videos, or get a background of the topic....you are going to love it...
Worked for me😃
Could you share that video? I am still confused about why the standard error should converge to 0 as the sample size grows instance of converging to the standard deviation of the population. Thank you
honestly im in a stats class and im failing. im in my final year of university and i dont think ill pass due to stats :(( i dont get it at all...and i hate that i have to take it when i will NEVER use it in my field of work..makes me hate stats even more....and i hate that everyone understands these videos and i dont understand a freaking thing hes saying
Well did you take up a stats job?....it's been 6years dude
The standard error (SE) of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation. If the parameter or the statistic is the mean, it is called the standard error of the mean (SEM) - Wikipedia
So for this video, a. Standard Error of the Mean is equal to the Standard Deviation of the Sampling distribution i.e. (Standard Deviation of the original distribution / √n) where n is no. of samples.
this is so helpful, thanks 😊
Thank you Sal for this explanation video and simulation.
@nazirdjon The probability distribution is the probability of taking a certain value in a sample space. e.g. for a die you have 1/6 probability for each outcome 1-6.
The standard deviation is the average of the squared difference between the mean and the observations.
This was so confusing :S
Yeah I know exactly what you mean. But when you learn the central limit theorem, statistics makes allot more sense. Try and learn this first and maybe it might help.
Awesome! Is the simulation available? I want to try it out.
This guy confuses me so much yet everyone tells me he's the best. Think the colourful drawing spaz my brain out
Statistics isn't an easy topic.
its true. its the material. he says it just like my stats teacher - it helps to write out each term and see the differences.
"sometimes this can get confusing" ~LOL
Hello Sal
I just got super confused by the two topics in the section of Sampling Distributions. Those two topics are-
1) Sampling Distribution of Sample proportion
2) Central Limit Theorem
They both seem to give a normal distribution shaped distribution with large sample size. The formula of mean is same for both but the formula of std deviation of the sample is different for them.
It would be a great help if you could explain the basic difference between them?
I think eventually that is what will happen. People will make videos on subjects that are so concise and easy to understand that they will be the most efficient and productive means of teaching. With the following generations having to know more and more (as humanity itself learns more), it just makes sense that education will go in this direction. :)
Good job !! Thanks! (from a Belgian UGent student)
This was excellent. Thanks, Sal!!!
Well put and exactly describes my teacher as well.
this is much better than Duke's coursera class on central limit theorem
When do we have to use the estimated population standard deviation from the sample, using Bessel's correction, instead of the sample standard deviation?
This was great! How do you estimate the SEM when you do not know the SD of the original distribution? Any good techniques for determining bounds?
this video was awsome... clear concept
Thank you very much for this video. Having studied statistics for so many years and never actually understood the intuition of this formula. You helped me a lot. BTW, I think you made others people's head explode by repeating so many times "standard deviation of the sampling distribution of the sample mean" xD
14:36 sampleception!
QUESTION:
When you make the simulation and the simulator tells that the standard deviation (sd) of the sample mean is 2.33. That was calculated with the standard error formula? Or was calculated with the standard deviation formula?
this is an awesome video! can I ask a question tho why is there a formula says the standard error = sqrt(n)* the standard deviation of the original sample?? as n is the draw number. I thought it should be the standard deviation/sqrt(n) like you said??
Makes it nice & clear !
Great stuff...but we need confidence intervalls as well, pretty please with sugar on top? Also, queue theory would be great as well, I realy need to brush up on my birth-death processes
understood! thanks a lot!!
what is 'n' here n the formula... n is 1. number of samples for 1 standard deviation calculation or 2. is it the number of time that the calculation of standard deviation that was repeated ???
Thank you so much sir!
good understanding video. it's better you can do a video on proof of the standard deviation of sample mean becomes that formula.
Question - doesn't central limit theorem apply only to larger samples (>30)?
An amazing explanation!
Good for you buzwazfuz! Not everybody can handle that. You could teach yourself perhaps - if so you could zoom along at your own pace. If you think you can do that talk to your teacher about doing independent study.
i don't get what is distribution and what is deviation:
deviation vs distribution. urgh
doesn't 2.325 round up to 2.33?
Not in stats it rounds down
The people at Khan Academy need to learn to spit it out.
Which software you're using in example
himanshu mishra Smooth Draw Software
This concept is quite tricky to grasp
Thankkss
Maybe I'm missing something, but why is it the population variance over n and not over (n - 1) like the formula for sample variance shows in some of Khan's other videos. I'm confused when to use and not use n-1...
Does standard error have units?
12:24 remember that calculator from years past 📟😇
Standard deviation of the sampling distribution of the sample mean
Could you do a video on t-distribution, confidence intervals please?
THANK YOU!
thank you for your video, it helps my comprehension about this concept
If you plot the mean of all the possible combinations of sample n from the population, you will get the normal distribution with the mean equal to the population. You don't have to reach infinity.
Sir, please help in solving this....
for the following data, calculate the standard error for mean when the sample is drawn under without replacement scheme. number of motor cycle accidents is 4.1 in a random examination of 8 cases out of 2500 with standard deviation being 0.9
This was awesome!
I have a doubt. How would the dispersion of the sampling distribution of sample means compare to the dispersion of its corresponding population?
How mean is 5 every time... How to calculate it?
Khan is awesome
Hello, shouldn't the numerator be SD of the sample, rather than SD of the population divided by sample observations,..apologies if i am missing something?
very helpful.!