Standard deviation larger than mean

[Vandana]

Hello

I've been running simulations and the ouput of my simulations is in a
form of distribution. When I compute the mean & standard deviation of
the output, I find that the standard deviation is much larger than
mean. Im not much of a statistics person and Im unable to comprehend
this.
Can somebody help me figure this out?

Thanks
Vandana.

[randovaro]

A standard deviation much larger than the mean is certainly possible.
It could be, for example, that your data are highly skewed. E.g. take
the simple dataset 42, 50, 55, 999. The outlier makes it very skewed
and the dataset has a mean of 287 but a st.dev of 475.

Standard deviation is a measure of the spread of your data. You can
also calculate skewness (a measure of asymmetry) & kurtosis (measure
of how "peaked" your dataset is). But I suggest first try plotting
your data (e.g. in the form of a histogram) to get a better idea of
its distribution.

[Gus Gassmann]

Not much to figure out. If you simulate from a distribution whose true
mean is zero, you _expect_ the (sample) standard deviation to be much
larger than the (sample) mean. Do you observe negative values in your
simulation?

[TechBookReport]

This is not that unusual. Perhaps you need a refresher on what standard
deviation is about? There's a basic non-mathematical explanation here:
http://www.techbookreport.com/tutorials/stddev-30-secs.html

HTH

[z]

you see that kind of thing all the time in real life, with things like
distribution of income, hospital stays, medical costs, etc. if the
distribution is Poisson, the sd=the mean. but if the distribution is
more wide than Poisson, the sd > the mean. which is the case more
often than not.
that's aside from when you have a lower mean because some values are <
0, of course.