Answer: Choice A) sqrt(2)
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Explanation:
Add up all of the values
13.3+14.3+15.3+16.3+17.3 = 76.5
Then divide by 5 as there are n = 5 values in the set given
76.5/5 = 15.3
The mean of this data set is 15.3
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Subtract the mean from each value to get this list of differences
x1 - mean = 13.3 - 15.3 = -2
x2 - mean = 14.3 - 15.3 = -1
x3 - mean = 15.3 - 15.3 = 0
x4 - mean = 16.3 - 15.3 = 1
x5 - mean = 17.3 - 15.3 = 2
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Square each result from the previous section
(-2)^2 = 4
(-1)^2 = 1
(0)^2 = 0
(1)^2 = 1
(2)^2 = 4
Then add up those results
4+1+0+1+4 = 10
This is the sum of the squared differences.
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Divide the sum of the squared differences by n = 5 to get 10/5 = 2
The population variance is 2
The population standard deviation is the square root of this, so we get sqrt(2) as our final answer.
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Side note: This data set was fairly small, so computing the standard deviation by hand wasnt too painful. When it comes to larger data sets, it is smarter to use a spreadsheet program to easily calculate the answer. The drawback is that you wont be able to get an exact answer in terms of radicals (then again you could always use a CAS, which stands for "computer algebra system").
