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I'm not a math or statistics expert and only have a self-taught basic understanding of these things. I'm working on a problem where I know the mean of the population and I want to estimate the standard deviation. This assumes a normal distribution of the population. Is this possible?

For example, if the mean if 32, with possible values between 0 and 100, can I calculate what the standard deviation is with just this information?

Thank you for your help!

Zigrivers
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  • Is the mean just a given? or was it calculated from data? If you have access to the data, estimating the shape of the distribution is just a few steps of R codes away. – horaceT Jun 16 '16 at 16:57
  • It is calculated from data, but I don't have immediate access to the data. So the real world example of this is if an organization of 100 sales reps has a win rate of 32%. My client can tell me that their win rate is 32%. What I want to be able to do is estimate the percentage of their reps that have win rates in different ranges using standard deviations (e.g. so we can focus on who needs help, who are our model sales reps, etc.).

    Eventually, I'll have access to the individual data and can do the calculations with all of the data, but it would be great if I could estimate it first.

     – Zigrivers Jun 16 '16 at 17:00
  • No, you can't get the standard deviation from the mean unless it's a special case such as Poisson distribution. – Aksakal Jun 16 '16 at 20:48

2 Answers2

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Normal distributions with very different standard deviation can have the same mean, so knowing the mean doesn't tell you which standard deviation you had. Indeed for samples from the normal distribution, the sample mean and sample standard deviation are independent, so the mean doesn't tell you anything about the standard deviation.

if the mean if 32, with possible values between 0 and 100

Then you cannot have a normal distribution (normal distributions are necessarily unbounded). On the other hand, the mean and the two bounds together do impose an upper limit on the standard deviation, but it's pretty weak.

Glen_b
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  • That's a great point and should have been obvious to me. It is indeed a Skewed Distribution curve. With it being a skewed distribution, is there any way to estimate the standard deviation? Or do I need the individual values to be able to calculate the standard deviation? – Zigrivers Jun 16 '16 at 16:27
  • While skewness would also indicate non-normality, it could well have been perfectly symmetric yet we would still know - for certain - that the distribution from which your sample was drawn could not actually be a normal distribution. 2. Saying that it's skewed doesn't really help us pin down the standard deviation. ... but the fact that you were able to go back and check that it was skewed clearly indicates you have an additional source of information than the mean. ... ctd
    • – Glen_b Jun 16 '16 at 23:09
  • ctd... Please include all available information about the numbers and what they measure, including any graphical displays if possible, in the text of your question (via an edit) and if you would be so kind, also comment here (and under the other answer) to indicate any substantive changes. You should also include what you're ultimately trying to achieve (why do you need to know the standard deviation?) ... @Zig – Glen_b Jun 16 '16 at 23:09