# 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)?

• Are you looking for a sort of confidence interval for the standard deviation?
– gary
Aug 4, 2011 at 14:47
• Yes, although that is part of the problem--I want to express how much the throughput varies. Aug 4, 2011 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, 2011 at 15:22
• @gary - thanks, I'll take a look! Aug 4, 2011 at 16:38