Can a data set with two or three numbers have

Kaspaueru2 2022-01-17 Answered
Can a data set with two or three numbers have a standard deviation?
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Expert Answer

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 x=x1=x
The standard deviation: σ=i=1i=n(xix)n
In this case n=1 so the formula is reduced to: σ=xx1=0.
1. Let A be a set of 4 numbers: A={2,3,5,8}
The mean x=2+3+5+84=184=4.5
The deviation would be:
σ=(24.5)2+(34.5)2+(54.5)2+(84.5)24
σ=2.52+1.52+0.52+3.524
σ=6.25+2.25+0.25+12.254
σ=214=5.252.29
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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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