Question

Compute the standard deviation for the set of data. 13.3, 14.3, 15.3, 16.3, 17.3

Answer 1

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").