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September 13th, 2015, 09:53 PM  #1 
Newbie Joined: May 2015 From: Portland, OR. USA Posts: 8 Thanks: 0  Shortcut Formula for the Unbiased Estimator
Hi everyone, I'm supposed to use the shortcut formula for the unbiased estimator to compute variance and standard deviation for this data set: 7, 37, 3, 8, 48, 11, 6, 0, 10, 3 Here's what I did: 1) Find X = 133 2) Find X^2 = 4061 3) Use the formula s^2 = 10(4061)  (133^2) / 10 (101) =20628.9 The book gave the answer for the variance as 254.7. I don't understand what I did wrong here. Can anybody help? 
September 14th, 2015, 10:28 AM  #2 
Senior Member Joined: Mar 2011 From: Chicago, IL Posts: 214 Thanks: 77 
$\displaystyle Mean=\frac{7+37+3+8+...}{10}=13.3$ Difference from mean: 713.3, 3713.3, 313.3, 813.3,...= 6.3 , 23.7 , 10.3 , 5.3 ,... $\displaystyle Variance=\frac{(6.3)^2+23.7^2+(10.3)^2+(5.3)^2+...}{101}\approx 254.7$ 
September 14th, 2015, 02:33 PM  #3  
Global Moderator Joined: May 2007 Posts: 6,640 Thanks: 625  Quote:
s^2 = (10(4061)  (133^2)) /( 10 (101))  

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