SOLUTION: Variance and standard deviation for 7, 8, 9, 6, 9, 12, 22, 15

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Question 715886: Variance and standard deviation for 7, 8, 9, 6, 9, 12, 22, 15
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Mean=%286%2B7%2B8%2B9%2B9%2B12%2B15%2B22%29%2F8=88%2F8=11

So xbar+=+11

Sample Standard Deviation: where is the average, is the ith number, and is the number of numbers

So we can replace N with 8



Subtract 8-1 to get 7



Replace with 11



Expand the summation (replace each x%5Bi%5D with the respective number)




Subtract the terms in the parenthesis



Square each term

sqrt%28%281%2F7%29%2825%2B16%2B9%2B4%2B4%2B1%2B16%2B121%29%29

Add up all of the terms

sqrt%28%281%2F7%29196%29

Multiply

sqrt%2828%29

Take the square root

5.29150262212918 This is is the sample standard deviation


The sample variance is simply the square of the sample standard deviation, so the sample variance is 28.