I am a Ph.D. candidate in the behavioural sciences and I am a bit at a loss with respect to finding a solution to the problem to follow:

I have the means and standard deviations of three time points in a sample of twenty people.

Mean (SD)

10.3 (2.4)

9.2 (1.3)

9.5 (1.8)

I want to calculate the area under the curve for these points. Each point is separated by 20 minutes.

((10.3+9.2)*20)/2+((9.2+9.5)*20)/2 = Area under the curve

Simple enough. The thing I'm struggling with, though, is how to calculate the variance, or the standard deviation, of area under the curve with only the SD of each time point and the sample size. I'm interested not only in the value, but in the formula used to estimate the variance (if it is statistical, is there a name for the equation? If it is mathematical, could you present the formula?)

This may or may not be an elementary question, but any help on this would be greatly appreciated.