# Std dev is different depending on the scale?

1. Jun 10, 2010

### Lobotomy

hello
std dev is the square root of the variance.

assume we measure lenghts of something normally distributed. we use millimeter.
we calculate our variance to be 100mm and thus std dev to be sqrt(100)=10mm

but, if we instead would measure the same objects in meter, then we'd get the variance to be 0.1m (exactely the same as 100mm) but then the std dev is sqrt(0.1)=0.3162 which is 316mm!

so have our std dev suddenly increased from 10mm to 316mm just by using a different scale when measureing the same objects?

2. Jun 10, 2010

### Office_Shredder

Staff Emeritus
Your variance would be 100 mm2 not just mm (you should check that the units of variance is that of the variable squared), so when converting to mm you need to convert to mm2

Otherwise when you took the square root your standard deviation would have units square root of a meter, which is pretty weird

3. Jun 10, 2010

### Lobotomy

ok i see. thanks.

so first time we had a variance of 100mm^2 and std dev of 10mm
then we measure in meter.
so that means we have a variance of 0.0001 m^2 (0.0001m^2=100mm^2).
so we calculate the std dev sqrt(0.0001)=0.01 which is equal to 10mm! makes more sense