My Math Forum Shortcut Formula for the Unbiased Estimator

 Probability and Statistics Basic Probability and Statistics Math Forum

 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 (10-1) =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: 7-13.3, 37-13.3, 3-13.3, 8-13.3,...= -6.3 , 23.7 , -10.3 , -5.3 ,... $\displaystyle Variance=\frac{(-6.3)^2+23.7^2+(-10.3)^2+(-5.3)^2+...}{10-1}\approx 254.7$ Thanks from statssav
September 14th, 2015, 02:33 PM   #3
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Quote:
 Originally Posted by statssav 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 (10-1) =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?
s^2 = (10(4061) - (133^2)) /( 10 (10-1))

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