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

Nov 26, 2015

Set 1: $\left\{1 , 2 , 3 , 4 , 5 , 6 , 7\right\} \textcolor{w h i t e}{\text{XXXX}}$Set 2: $\left\{10 , 20 , 30 , 40 , 50 , 60 , 70\right\}$
${\sigma}_{\text{Population")("Set 1") = 2color(white)("XXXXX")sigma_("sample")("Set 1}} = 2.160$
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 (${\sigma}_{\text{pop}}^{2}$) as the sum of the squared differences divided by the number of data values.
• Calculate the population standard deviation(${\sigma}_{\text{pop}}$) 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 (${\sigma}_{\text{sample}}^{2}$) as the sum of the squared differences divided by 1 less than the number of data values.
• Calculate the sample standard deviation(${\sigma}_{\text{sample}}$) as the primary square root of the population variance.

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