MarinStatsLectures-R Programming & Statistics
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!
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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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awesome
Very useful! And I'm curious about how did this professor write on the translucent board? Write in the opposite direction?
👋🏼 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.
If you like to support us, you can Donate (https://bit.ly/2CWxnP2), Share our Videos, Leave us a Comment and Give us a Like 👍🏼! Either way We Thank You!
what is this Property A) & B) that you are using? What does X mean?
Thank You for the video..
it's really helpful.
Hello! I don't understand what x1, x2…xn correspond to.. Do they represent the different means of the n samples taken from a population? And if yes, why do we assume that their standard deviation is σ? Thank you.
Thank you
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, (sigma2)2…… Are they all equal?
Thanku
It helped me!
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?
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?
Hi. I am still not clear on Xi. in some of the comments you say that Xi is an observation, e.g. X1 could be a person with height 170cm. how could we say that a person has a mean and a variance associated with it. I thought mean and variance are properties of a sample (or a population) and not the individual observations.
How can one observation have a mean or a variance? Aren't those properties of samples with more observations? I am confused. Do you have a video explaining this? Thank you
Excellent and important lecture, thanks for including it in your playlist – also, very unique and enjoyable humour re: var typo!
I am a bit confused about what it means to take the variance of x_1, x_2 etc. individually. Aren't x_1, x_2… individual observations? How can a value/observation have a variance (e.g., Var(x_1))? I thought the variance should describe a distribution rather than an observation
Why not (n-1) in this case for standard deviation of sample mean?
When you say "all of the Xi have the same mean and variance", I don't understand what that means.
For example, if I have a random variable X, from 1 to 100. And I take multiple sample sets of 5. All of the sample sets will have different means and the variance of that we get from the standard error of means formula.
But I'm still stuck on the part about all the Xi having the same mean. So X1 will be 1. X50 will be 50. What do you mean when you say they have the same means, individually?
And if Xi is supposed to represent sample sets, I don't see how it would have the same means…
Anyone in the comments feel free to help :)))))))))))))))))))))))))
Thank you so much! it's very useful!
thank you! it's very helpful especially most of the textbooks just give the formulation without prove process.
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 clarify…….
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. 😉
Thank you for this wonderful video.
Thank you so much!