# Estimated varaince of sample data

1. Oct 3, 2014

### somecelxis

1. The problem statement, all variables and given/known data
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 cant i use this way? my ans for second way is 19051. which is wrong....

2. Relevant equations

3. 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

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2. Oct 3, 2014

### 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 3. The attempt at a solution

(Basically, your <x2> is wrong. )

3. Oct 3, 2014

### somecelxis

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

4. Oct 3, 2014

### BvU

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

5. Oct 3, 2014

### 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.

6. Oct 3, 2014

### Ray Vickson

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

7. Oct 3, 2014

Seconded.

8. Oct 3, 2014

### 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

9. Oct 3, 2014

### 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.

10. Oct 3, 2014

### 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 ?

11. Oct 4, 2014

### somecelxis

thanks all, i managed to solve the question above.
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