N=2 mean and SD

[peterchi]

Hope this is an appropriate forum for this.

My mom asked me the following question:
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Peter,

I have a statistics question:

As I understand, when I have 3 samples (N=3) and above, I can have mean and standard deviation. How about If N is 2? Can I have SD too?

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This was my response:
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technically you can, but it is not very meaningful. standard deviation is a measure of the distance of the observations away from the mean. if you only have two observations, they are always equidistant from the mean since the mean will be exactly between the two observations. calculating the standard deviation will not tell you anything more about your data than you would know by just looking at the two observations.

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Did I give a good answer? Just wanna check myself, I'm assuming she needs to know this for work so I don't want to give a wrong answer.

[alThor]

[ QUOTE ]
As I understand, when I have 3 samples (N=3) and above, I can have mean and standard deviation. How about If N is 2? Can I have SD too?

[/ QUOTE ]

You continue to estimate SD using the same formula, sum (x_i - mean)^2 / n-1 .

If you want to see how much you can trust this estimate, use the chi-square distribution to make a confidence interval. With n=2, it's going to be a big one. Google it for more info.

[ QUOTE ]
calculating the standard deviation will not tell you anything more about your data than you would know by just looking at the two observations.

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I'm not sure what that sentence is supposed to mean. (That's a polite way of saying it doesn't really mean anything.)

In the real world, I can't imagine an example where you need to estimate a SD but find yourself limited to n=2. Is this just a theoretical question?