Question

What are the standard deviations of {1, 2, 3, 4, 5, 6, 7} and {10, 20, 30, 40, 50, 60, 70}?

Answer 1

Set 1: `{1,2,3,4,5,6,7}color(white)("XXXX")`Set 2: `{10,20,30,40,50,60,70}`
`sigma_("Population")("Set 1") = 2color(white)("XXXXX")sigma_("sample")("Set 1") = 2.160`
`sigma_("population")("Set 1") = 20color(white)("XXXX")sigma_("sample"_(Set 2) = 21.60`

Explanation:

Which Standard Deviation values you get depends upon whether the data is taken to be the entire population or just a sample from the population.

A mathematics calculator or a spreadsheet can be used to provide these standard deviation values directly.

Continue beyond this point only if you want/need to be able to do these calculations by hand:

• Find the *mean of the data values (sum divided by number of data values)
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• For each data value
• • Calculate the difference between the data value and the mean
• • Square the difference

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• If the data values are the entire population
• • Calculate the population variance (`sigma_("pop")^2`) as the sum of the squared differences divided by the number of data values.
• • Calculate the population standard deviation(`sigma_("pop")`) as the primary square root of the population variance.

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• If the data values are a sample from the population
• • Calculate the sample variance (`sigma_("sample")^2`) as the sum of the squared differences divided by 1 less than the number of data values.
• • Calculate the sample standard deviation(`sigma_("sample")`) as the primary square root of the population variance.

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