# Math Help - standard deviation

1. ## standard deviation

Hi,

sorry if this is a silly question, but I am trying to decide whether a standard deviation of 0.8 would be considered a small one, if the the mean is 3.0. Is there some kind of rule for what would be considered a small standard deviation, relative to the size of the mean?

walt

2. ## Re: standard deviation

I wouldn't try to make any sweeping rule, not least because you can induce any relationship you want between mean and standard deviation by a flat transformation of data.

To see the significance of that, suppose you have some temperature data. The relationship between mean and standard deviation will be very different depending on whether the same underlying figures are reported in celcius or farenheight.

3. ## Re: standard deviation

Ok, thanks, maybe it is just not possible to devise such a simple rule.

Originally Posted by SpringFan25
I wouldn't try to make any sweeping rule, not least because you can induce any relationship you want between mean and standard deviation by a flat transformation of data.

To see the significance of that, suppose you have some temperature data. The relationship between mean and standard deviation will be very different depending on whether the same underlying figures are reported in celcius or farenheight.

4. ## Re: standard deviation

Sorry, I realize that my question was slightly different from the one I originally posed. The question is, if the mean DIFFERENCE between treatment groups is 3.0 and the standard deviation is 0.8, is this a small standard deviation, compared to the mean DIFFERENCE?

thanks again in advance
walt

Originally Posted by walt415
Ok, thanks, maybe it is just not possible to devise such a simple rule.