what is the standard deviation of an empty set? is it undefined or zero?

Interesting question. I’d opt for undefined. The snide answer would be “It’s the same as the mean of an empty set” What is the context of the question - I mean, why would you care about the SD of an empty set?

The real challenging question is what is the standard deviation of the standard deviation of an empty set, belonging to an emptier set?

standard deviation is defined for a random variable not for a set.

That’ll teach you to take drugs and post on AF.

bchadwick Wrote: ------------------------------------------------------- > Interesting question. I’d opt for undefined. > > The snide answer would be “It’s the same as the > mean of an empty set” > > What is the context of the question - I mean, why > would you care about the SD of an empty set? GMAT-ing. just wondering. SD of a one element set is 0. So I wondered what the SD for an empty set would be.

I think since you are dividing by N, and N in this case would be 0, the SD of an empty set would be undefined.

My standard deviation involves whipped cream and hand cuffs. I have some non-standard deviations as well.

it should be 0 but no one will ever ask you that on the gmat exam