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

1 Answer
Oct 29, 2015

Yes it can.

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:

  1. A sigle number would have a deviation of zero:

Let #A={x}# be a data set with only a single value.

The mean #bar{x}=x/1=x#

The standard deviation: #sigma=sqrt((Sigma_{i=1}^{i=n}(x_i-bar(x)))/n)#

In this case #n=1# so the formula is reduced to: #sigma=sqrt((x-bar(x))/1)=0#.

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

The mean #bar(x)=(2+3+5+8)/4=18/4=4.5#

The deviation would be:

#sigma=sqrt(((2-4.5)^2+(3-4.5)^2+(5-4.5)^2+(8-4.5)^2)/4)#

#sigma=sqrt((2.5^2+1.5^2+0.5^2+3.5^2)/4)#

#sigma=sqrt((6.25+2.25+0.25+12.25)/4)#

#sigma=sqrt(21/4)=sqrt(5.25)~~2.29#