Standard Error of the Mean: Concept and Formula | Statistics Tutorial #6 | MarinStatsLectures

Standard Error of the Mean, Concept and Formula: What is the standard error of the sample mean in statistics and what does it show? Why does Standard Error formula equal to Standard deviation Over Square Root of n? Step by Step Explanation!

In this statistics video tutorial we will learn why the Standard deviation of the Mean (or the Standard Error of The Mean) is equal to the standard deviation divided by the square root of the sample size.

While the formula for Standard Deviation of mean is presented as ''sigma over root n'', this often appears as a 'magical' result! here, we spend a few minutes deriving the formula and explore where it is coming from. We do this in a separate video so that we can provide justification for why this is the formula, while not letting that derivation become a distraction when presenting topics that make use of the standard deviation of the mean.

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Our Team:
Content Creator: Mike Marin (B.Sc., MSc.) Senior Instructor at UBC.
Producer and Creative Manager: Ladan Hamadani (B.Sc., BA., MPH)

These videos are created by #marinstatslectures to support some statistics and R programming language courses at The University of British Columbia (UBC) (#IntroductoryStatistics and #RVideoTutorials for Health Science Research), although we make all videos available to the everyone everywhere for free.

Thanks for watching! Have fun and remember that statistics is almost as beautiful as a unicorn!

[marinstatlectures]

👋🏼 hello there! In this video we will learn why the Standard deviation of the Mean (or the Standard Error of The Mean) is equal to the standard deviation divided by the square root of the sample size.

[rubenpinto]

Excellent and important lecture, thanks for including it in your playlist - also, very unique and enjoyable humour re: var typo!

[joannenicole]

okay, this is the first time i've ever watched any of his videos, but wow that was good! i still can't get over how he can write backwards so easily! it was so easy to understand and made me remember why math induction was so satisfying! thank you so much, Mr Marin!

[somdubey]

Loved the way you converted a typo into a learning. Hats off. The topic cannot be more clearer than presented in the video.

[Doctor_CCC]

Thank you for this helpful video. The only thing that isn't clear to me is the reason you replace sigma (population SD) with s (sample SD) in the formula?

[shortly]

Hi,

The "n" which comes out in the end refers to the no. Of samples or observation.
However, while solving problems we always consider it as sample size.

Both of them appears to be different.

Please

[hectormiguelvinuezabarroso]

Thank you, with this video I understood where the standard error of the mean comes from.

[RegularObamahedron]

Very clean explanation. Thank you so much!

[RaviShankar-pkis]

@marinstatlectures, how is the VAR(X1)=VAR(X2)=...=sigma?

[jbergamp]

Do you have a video probing the first property you assumed here?. Thanks

[AlbertoLugli]

Thank you for this contribute, very interesting!

Does anyone know why at 3:38, when variance get substituted for the standard deviation, all of the standard deviations becomes equal? Shouldn't they be different, because they come from different samples?

Trying to grasp this more intuitively than the algebraic way. ;)

[marcoventura]

Another great video from Mike Marin. Thank you!

[vishalahuja]

Hi Marin, great explanations! One question though: why is it that X_i has mean mu, and not mu_i. Same for variance: why sigma, and not sigma_i ?

[ningyanzhang]

thank you! it's very helpful especially most of the textbooks just give the formulation without prove process.

[adarshjamwal]

Thank you so much sir, but I have a query .why you not make practical by using any programming language?

[linezero]

why is the variance of x_i sigma^2? so in other words, why is the variance of a single value the standard deviation of the sample?

[DJ-yjvg]

so is this assuming there is only 1 sample of n data points? and that particular sample has a standard error given by this formula? Some books talk about taking multiple samples and calculating the mean of these individual means of each sample...

[孙甜甜-yf]

Very useful! And I'm curious about how did this professor write on the translucent board? Write in the opposite direction?

[Cuicui]

Thank you so much! it's very useful!

[Sthitadhi]

Thanks a lot, Dr. Marin, for this helpful video! The only thing that isn't clear to me is the reason you wrote, Var(X1), Var(X2) and so on equals to sigma2 and not (sigma1)2, Are they all equal?