Can a data set with two or three numbers have a standard deviation?

Question

Maricela Alarcon · Accepted Answer

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

\overset{―}{x} = \frac{x}{1} = x

The standard deviation:

σ = \sqrt{\frac{\sum_{i = 1}^{i = n} (x_{i} - \overset{―}{x})}{n}}

In this case n=1 so the formula is reduced to:

σ = \sqrt{\frac{x - \overset{―}{x}}{1}} = 0 .

1. Let A be a set of 4 numbers: A={2,3,5,8}
The mean

\overset{―}{x} = \frac{2 + 3 + 5 + 8}{4} = \frac{18}{4} = 4.5

The deviation would be:

σ = \sqrt{\frac{{(2 - 4.5)}^{2} + {(3 - 4.5)}^{2} + {(5 - 4.5)}^{2} + {(8 - 4.5)}^{2}}{4}}

σ = \sqrt{\frac{{2.5}^{2} + {1.5}^{2} + {0.5}^{2} + {3.5}^{2}}{4}}

σ = \sqrt{\frac{6.25 + 2.25 + 0.25 + 12.25}{4}}

σ = \sqrt{\frac{21}{4}} = \sqrt{5.25} \approx 2.29

Neil Dismukes · Accepted Answer

Explanation: Yes. It is possible to calculate the standard deviation of any non empty set of numbers.

Can a data set with two or three numbers have

Answered question

Answer & Explanation

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