Why is the Variance of the Sample Mean equal to Sigma^2/n ? How to find the Variance of X-bar

[DANIEL-bher]

Had this is my assignment and didn't know how to do it, but now I get it, Thanks a bunch.

[RoseMbabazi-xj]

Thank you for improving my poor maths, i have been struggling to understand this in "Tests of significance"in biostatistics

[Gabric_]

Lovely explanation, very clear. Only a doubts: which is the easiest demostration that Var(ay)=a^2var(y)? (I just subscribed, thank You)

[KiranPatel-wljz]

Please could you explain at 3:30 why Var(xi) = σ^2 rather than s^2 ? Isn't σ^2 the population variance, but xi is defined from i=1 to n so isn't it a sample?
Or is the population only defined from i=1 to n?

[chungachilu]

Thank you for the video, very helpful. What if the equation is like Var (X ̅) = 1/n ∑Var (Xi) ?

[sagneekdutta]

Thank you a lott
I was struggling to understand this

[hungarogames]

Am I right, that this works only when the distribution of the variables are the same?

[sadharanInsaan]

Mam, Do we need to assume that the random vars are independent?

[rishibhardwaj]

Hi
Thankyou for this insightful video! Can you please share which book or research paper you referred to?

[Titurel]

Please explain why the constant gets squared Var(ay)=a^2Var(y)

[jambulwhae]

hi sis, im sorry, I want to ask, what if the question asked is Var(Xbar/2)? is the output a sigma^2/4n?

are you willing to explain to me?

[weirdlines]

Great video! Do you know how one could get that formula by starting with Chebyshevs-inequation?

[nicolas]

I think the proof is wrong since proposition Var(Xi) = sigma^2 i={1, 2, ...n} is not correct, keeping in mind that sigma^2 is actually the population variance, which by definition differs from the deviation of every single Xi (except if Xi=c for all i)