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September 13th, 2015, 08:53 PM   #1
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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?
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September 14th, 2015, 09:28 AM   #2
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$\displaystyle Mean=\frac{7+37+3+8+...}{10}=13.3$

Difference from mean:
7-13.3, 37-13.3, 3-13.3, 8-13.3,...=
-6.3 , 23.7 , -10.3 , -5.3 ,...

$\displaystyle Variance=\frac{(-6.3)^2+23.7^2+(-10.3)^2+(-5.3)^2+...}{10-1}\approx 254.7$
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September 14th, 2015, 01:33 PM   #3
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Quote:
Originally Posted by statssav View Post
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?
Your formula is missing a pair of parentheses. It should read:
s^2 = (10(4061) - (133^2)) /( 10 (10-1))
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