# calculating and interpreting SD from mean and SEM

##### New Member
I have some summary stats on people's drink intake and I'd like to work out the variance.

Frustratingly I have no access to the full data set so I'm having to infer the shape as much as possible from a handful of descriptive stats.

I have access to the mean amount, the standard error of the mean and the weighted and unweighted bases (segmented by sex, age, etc.)

I am guessing I can calculate SD for each segment by multiplying the sqrt of the unweighted base (i.e. actual sample size) by the SEM.
Is this valid, or is there something I've overlooked?

If one SD is significantly greater than the mean, what can I hypothesise about the skewness of the underlying data set? Bearing in mind I know there are no null values (non-drinkers were excluded)...

Based on my knowledge of the population involved, my assumption is that the bulk of the sample will have a relatively low intake, with a long narrow tail of people drinking up to several times the 'normal' amount. I'd like to be able to point to the variance to support this assumption.

#### spunky

##### Doesn't actually exist
I have access to the mean amount, the standard error of the mean and the weighted and unweighted bases (segmented by sex, age, etc.)
What are "weighted and unweighted bases"?

I am guessing I can calculate SD for each segment by multiplying the sqrt of the unweighted base (i.e. actual sample size) by the SEM. Is this valid, or is there something I've overlooked?
I guess this depends on what you mean by a "base" and these weighting issues but if all you're doing is re-arranging the formula for the standard error of the mean so that it looks like $$\sigma_{\bar{{x}}}\sqrt{n} = \sigma$$ then, sure, I don't see any problem with that to obtain the standard deviation from the standard error of the mean.

If one SD is significantly greater than the mean, what can I hypothesise about the skewness of the underlying data set? Bearing in mind I know there are no null values (non-drinkers were excluded)...
Generally speaking, no, you can't. For some distributions the mean and the higher moments are independent and for others not. A normal distribution could easily have a mean of 0, a standard deviation of a 1000 and it would still have 0 skewness.

Based on my knowledge of the population involved, my assumption is that the bulk of the sample will have a relatively low intake, with a long narrow tail of people drinking up to several times the 'normal' amount. I'd like to be able to point to the variance to support this assumption.
I'm sorry but without more information about the distribution I can't see how the variance alone or the relationship between the variance and the mean would tell you that.