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I am reading a textbook to learn more about statistics. This section is about estimating the mean of a population when standard deviation of the population is known.

My simple question is this: How can we know the standard deviation of a population without knowing the mean? My understanding is that to calculate the standard deviation you need to know the mean. Or is there some other way, i.e. without the formula, to calculate the standard deviation?

Any help is appreciated.

Thanks.

soroor
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    If you know only the standard deviation of some measurement on a population, you can't say anything whatsoever about the mean. What else do you know about the population? – John Aug 18 '14 at 18:54
  • There is a subtle difference between (mean,standard deviation) of a real population and (mean,standard deviation) of random variables that are used to make a mathematical model for this population. A good distinction between model and that what is modelled is important. I suspect that the 'known standard deviation' that you mention is the standard deviation of a random variable. – drhab Aug 18 '14 at 19:21
  • I hit return too soon. Sorry. Thanks for your replies. This section discusses estimating the mean of a population given the standard deviation of the population. It then proceeds to define confidence intervals. And finally we learn about the error margin and the confidence interval. There is additional info given and that is the mean of a particular sample of the population. Summary: given the sample's mean and the standard deviation of the whole population we are taught how to find a confidence interval for the mean of the whole of the population. – soroor Aug 19 '14 at 06:33

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Let's say you have a normally distributed random variable that you can't measure directly, but you CAN measure the difference between two of those variables. For example, you have two people measuring the exact same quantity (eg., two people timing the same race with stopwatches). Their measurements have error and you don't know the true value of the quantity of interest (eg., actual race time) but you have pairs of measurements of the identical quantity. If you assume the measurement error in a sufficiently large sample of timers is normally distributed, then you can use the measurement pairs to estimate the standard deviation of the measurement error even though you don't know the mean. Then you can use a separate experiment (with a much smaller sample) with more expensive equipment to estimate the mean measurement error given the known deviation.

B Factor
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