SOLUTION: how do you find the variance and standard of the following data? 12,8,13,9,13,11,12,11,9

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Question 196717: how do you find the variance and standard of the following data? 12,8,13,9,13,11,12,11,9
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Standard Deviation:

First sort the numbers into ascending order (from least to greatest):
8,9,9,11,11,12,12,13,13



Now let's find the mean:



To find the mean, add up all of the numbers and divide the sum by the number of numbers (which in this case is 9).
Mean=%288%2B9%2B9%2B11%2B11%2B12%2B12%2B13%2B13%29%2F9=98%2F9=10.8888888888889

So the mean is 10.8888888888889


Now let's find the standard deviation.


where is the arithmetic mean, is the ith number, and is the number of numbers

So we can replace N with 9 (since there are 9 numbers)



Replace with 10.8888888888889



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




Subtract the terms in the parenthesis



Square each term



Add up all of the terms

sqrt%28%281%2F9%2926.888889%29

Multiply

sqrt%282.98765433333333%29

Take the square root

1.7284832464717

So the standard deviation is 1.7284832464717


Since and is the variance, this means that the variance is: