1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Estimated varaince of sample data

  1. Oct 3, 2014 #1
    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
     

    Attached Files:

  2. jcsd
  3. Oct 3, 2014 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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. )
     
  4. Oct 3, 2014 #3
    my E(X^2) = 19159... why it's wrong? then what should it be?
     
  5. Oct 3, 2014 #4

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    It should not change by a factor of around 1000 if your sample is a factor 1000 bigger
     
  6. Oct 3, 2014 #5

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    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.
     
  7. Oct 3, 2014 #6

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Type out your formulas, so we can see what you are calculating.
     
  8. Oct 3, 2014 #7

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Seconded.
     
  9. Oct 3, 2014 #8

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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
     
  10. Oct 3, 2014 #9

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    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.
     
  11. Oct 3, 2014 #10

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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 ?
     
  12. Oct 4, 2014 #11
    thanks all, i managed to solve the question above.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted