Calculating variance from range

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Dawei
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Hello,

I have taken 5 samples and found that my average concentration is 5 mg, with a range of .003 mg in either direction. I would like to calculate the variance with only this information.

Is this possible? I am used to calculating the variance from the standard deviation, but I don't have this available.
 
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No, it's not possible. But if you know about the shape of the distribution you may be able to estimate the variance.
 
You can use the 5 sample data points to estimate the variance. Take the sum of the squares of the differences between the individual points and the average. Then divide by 4 (n-1 in general). This is an unbiased estimate for the variance.
 

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