Estimated varaince of sample data

[somecelxis]

Homework Statement

sample data as bellow:
46,48,51,50,45,53,50,48

to find the estimated varaince , the ans with 6.10 is correct... why can't i use this way? my ans for second way is 19051. which is wrong...

Homework Equations

The Attempt at a Solution

Var(x) = E(x^2) -( E(x)^2) = 19159- ( ((391/8) ^2 ) = 16670, then my s^2 = 16670...
i use the top part of the formula ,( 8/ (8-1) ) x 16670 = 19051

 

[BvU]

In the left shred that you should have retyped under 2. Relevant equations (in which case you would have seen your error) the recipe differs from what you type under

The Attempt at a Solution

(Basically, your <x²> is wrong. )

 

[somecelxis]

my E(X^2) = 19159... why it's wrong? then what should it be?

 

[BvU]

It should not change by a factor of around 1000 if your sample is a factor 1000 bigger

 

[Simon Bridge]

You can compute the variance of the sample - you don't have to estimate it.
Usually your are expected to estimate the variance of the population from the sample.
http://en.wikipedia.org/wiki/Variance#Population_variance_and_sample_variance

However, I cannot tell how you went wrong unless you show your reasoning and calculation.
But it looks like you, at least, have another step to go.

 

[Ray Vickson]

my E(X^2) = 19159... why it's wrong? then what should it be?

Type out your formulas, so we can see what you are calculating.

 

[Simon Bridge]

Type out your formulas, so we can see what you are calculating.

Seconded.

 

[BvU]

Hey guys, let's not all of us be so tough on this guy! He did present something under 3. and I try to point out to him that $E \ne \Sigma$ ...then he's done

 

[haruspex]

As BvU points out, you forgot part of the calculation of E[X²]. The other issue is you have to decide whether you are trying to find the actual variance of the sample or estimate the variance of the underlying population. Only the second involves the n/(n-1) factor.

 

[BvU]

Just for the heck of it, you have a very, very special sample here! Doesn't happen very often that $<x> = \Sigma (x - <x>)^2$ exactly !

By the way, is excelsis still here ?

 

[somecelxis]

mething under

thanks all, i managed to solve the question above.