# Can a data set with two or three numbers have

Can a data set with two or three numbers have a standard deviation?
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Maricela Alarcon
Explanation:
Yes. It is possible to calculate the standard deviation of any non empty set of numbers. However it would be difficult to interpret such value for such a small set of data.
Examples:
A sigle number would have a deviation of zero:
Let A={x} be a data set with only a single value.
The mean $\stackrel{―}{x}=\frac{x}{1}=x$
The standard deviation: $\sigma =\sqrt{\frac{\sum _{i=1}^{i=n}\left({x}_{i}-\stackrel{―}{x}\right)}{n}}$
In this case n=1 so the formula is reduced to: $\sigma =\sqrt{\frac{x-\stackrel{―}{x}}{1}}=0.$
1. Let A be a set of 4 numbers: A={2,3,5,8}
The mean $\stackrel{―}{x}=\frac{2+3+5+8}{4}=\frac{18}{4}=4.5$
The deviation would be:
$\sigma =\sqrt{\frac{{\left(2-4.5\right)}^{2}+{\left(3-4.5\right)}^{2}+{\left(5-4.5\right)}^{2}+{\left(8-4.5\right)}^{2}}{4}}$
$\sigma =\sqrt{\frac{{2.5}^{2}+{1.5}^{2}+{0.5}^{2}+{3.5}^{2}}{4}}$
$\sigma =\sqrt{\frac{6.25+2.25+0.25+12.25}{4}}$
$\sigma =\sqrt{\frac{21}{4}}=\sqrt{5.25}\approx 2.29$
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Neil Dismukes
Explanation: Yes. It is possible to calculate the standard deviation of any non empty set of numbers.