Is it possible to find the SD without the data?

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SUMMARY

The discussion centers on calculating the standard deviation (SD) from a known mean and a specific percentile value in a normal distribution. Given a mean of 3.8 and a 99th percentile value of 4.64, the standard deviation (σ) can be derived using the formula σ = (value at percentile - mean) / a, where a is approximately 2.33 for the 99th percentile. The calculated standard deviation is 0.36, which allows for estimating the 90th percentile value at 4.26. The invNorm function was utilized to confirm the accuracy of the standard deviation.

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stonecoldgen
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I have the mean and I have the value at a percentile (99th percentile to be specific). I am just wondering if it's possible to find the SD. Actually, what I am trying to find is the value at the 90th percentile (I think I need the SD to do it, but maybe just maybe there's another method...)


Just in case, the mean is 3.8 and the value at the 99th percentile is 4.64
 
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You need to know the shape of the distribution. If it is normal you can get the S.D. (σ)from the data given by looking up the value for a when aσ = .99. I get a ≈ 2.33, but I suggest you check it. σ = (4.64 - 3.8)/2.33.
 
Oh yeah, I forgot to say it's a normal distribution. I used the invNorm function to see which standard deviation best models the situation, so I found out that 0.36 does it pretty well. So the value I got for the 90th percentile is more of an estimate (4.26), but I think it fits well enough.
 

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