Kaspaueru2
2022-01-17
Answered

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

You can still ask an expert for help

Maricela Alarcon

Answered 2022-01-17
Author has **28** answers

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$\stackrel{\u2015}{x}=\frac{x}{1}=x$

The standard deviation:$\sigma =\sqrt{\frac{\sum _{i=1}^{i=n}({x}_{i}-\stackrel{\u2015}{x})}{n}}$

In this case n=1 so the formula is reduced to:$\sigma =\sqrt{\frac{x-\stackrel{\u2015}{x}}{1}}=0.$

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

The mean$\stackrel{\u2015}{x}=\frac{2+3+5+8}{4}=\frac{18}{4}=4.5$

The deviation would be:

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

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

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

$\sigma =\sqrt{\frac{21}{4}}=\sqrt{5.25}\approx 2.29$

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

The standard deviation:

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

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

The mean

The deviation would be:

Neil Dismukes

Answered 2022-01-18
Author has **37** answers

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

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