# Standard deviation of a rate

I am trying to measure the throughput of a network. I collected sample transfer times for 1,000 trials, and then calculated the arithmetic mean and standard deviation for the data (e.g., mean = 0.2s, stdev = 0.01s for 1GB of data).

It is easy to compute the mean throughput (e.g., 1GB / 0.2s = 5 GB/s). Is it possible to compute the standard deviation of the throughput directly from the standard deviation of the transfer time? Or do I need to use the original 1,000 data points (which would unfortunately need to be re-measured)?

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Are you looking for a sort of confidence interval for the standard deviation? – gary Aug 4 '11 at 14:47
Yes, although that is part of the problem--I want to express how much the throughput varies. – Chris Gregg Aug 4 '11 at 14:53
Well, maybe you can use the fact that your sample size is large-enough to use the CLT and construct a confidence interval using $\frac{s}{n^{1/2}}$ for the sample standard deviation, where s is the sample standard deviation. – gary Aug 4 '11 at 15:22
@gary - thanks, I'll take a look! – Chris Gregg Aug 4 '11 at 16:38