SD can be calculated using range, if yes which formula
max range-min range/4
0r
max range-min range/6
Hello Gyan,
"Range / k" formulas are, at best, potential estimators of SD, not computations for SD. In other words, there's no way to be certain what the true SD of a data set is, based on just the range (or the range and N of cases). So, such formulae should be used with an abundance of caution.
The value of "k" depends on the sample size. Bigger N in the sample size calls for larger denominators. The reason is, all other things equal, the larger the sample, the greater the likelihood of an extreme score (hence, a larger sample range).
However, you'll find that these methods make strong assumptions about the shape of the distribution in order for the estimates to even be in the ballpark.
Here's a link that walks through the adjustment of observed range to estimated SD, assuming normal distributions: https://influentialpoints.com/Training/using-range-to-estimate_sd.htm
What I found, using uniform distributions (e.g., 1, 2, ... N), is that the divisor of 3 works reasonably well for N of 4-16 cases, and 3.4 works reasonably well for N of 25-100 cases.
Good luck with your work.
Maybe, the only certain bounds can be constructed using Chebyshev's inequality. For the data similar to Normal (most concentration and least SD), Max-Min divided by 6 works. For the data similar to uniform (least concentration and most SD) a denominator between 3 and 4 works much better.
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