# Is it possible for a normal distribution to have mean 0 and standard deviation less than 1?

Is it possible to have a dataset having a normal distribution with mean close to 0 and standard deviation less than 1?

for eg, my dataset have mean 0.0004 and Standard deviation of 0.0089. The reason for asking this, is that normally the standardized normal dist have mean 0 and standard dev of 1.

• Just change the units of measurement. For instance, if these data are in kilometers, convert them to millimeters: the mean becomes $400$ and the standard deviation becomes $8900$. Although the mean is no longer "close to $0$" and the SD is definitely greater than $1$, your data haven't changed: we have only changed how they are described. Therefore there couldn't possibly be anything invalid about the original situation. – whuber Feb 16 '17 at 18:21
• FYI to help you visualize standardization... changing the mean "shifts" the graft to the origin (addition or subtraction, applied first), changing the s.d. by scaling it squeezes or broadens it (multiplication or division, applied 2nd). – Brad Thomas Feb 17 '17 at 5:00