use the degrees of freedom for the mean is N and for the variance it is N-1  b.because these denominators provde the most unbiassed estimates of Micro and  small alpha respectively. c.because the mean is the center of X and the variance is the average deviation from center d. because all X values ar

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Why is N the denominator of the formula for the sample mean while N-1 is the denominator for a sample variance?

a. because the degrees of freedom for the mean is N and for the variance it is N-1 

b.because these denominators provde the most unbiassed estimates of Micro and  small alpha respectively.

c.because the mean is the center of X and the variance is the average deviation from center

d. because all X values are used for computing the mean but one of the values of X is not used in computing variance

Expert Solution
Step 1

The formula for the sample variance is:

Statistics homework question answer, step 1, image 1

The sum of the deviations from the mean is always equal to zero because the sum of the deviations below the mean will always equal the sum of the deviations above the mean. 

That is why the N-1 is the denominator is used for a sample variance. The degrees of freedom for the mean is N and for the variance it is N-1 .
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