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

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) (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).

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 with the respective number)

Subtract the terms in the parenthesis

Square each term

Add up all of the terms

Multiply

Take the square root

So the standard deviation is

Since

and

is the variance, this means that the variance is:

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