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Table 1 The best formula for estimation by distribution.

From: Estimating the mean and variance from the median, range, and the size of a sample

Best Formula for Sample size (n) Mean Estimation Standard Deviation Estimation
  Formula (5) Median Formula (16) Range/4 Range/6
Log-Normal n ≤ 23 23 <n n ≤ 15 15 <n ≤ 64 64 <n
Beta n ≤ 30 30 <n n ≤ 15 15 <n ≤ 100 100 <n
Exponential n ≤ 21 21 <n n ≤ 15 15 <n ≤ 66 66 <n
Weibull n ≤ 25 25 <n n ≤ 16 16 <n ≤ 110 110 <n
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