Is it possible to compare the two data sets with same sample number say 50, mean 27.5 and Range 50 from one another ? Like, will they have same standard deviation or we just can't compare their standard deviation from given information.
[Math] Standard deviation of two data sets
standard deviationstatistics
Best Answer
If all you have if range and mean, you will be able to say very little about the standard deviation. You should be able to calculate a minimum standard deviation (by setting two values to the extreme and the rest to the mean) and a maximum possible standard deviation (by setting all values to one of the two extremes), but beyond that there will be very little you can do.
As an exercise to see this, consider the set that has 48 elements equal to $27.5$, one element equal to $2.5$ and one element equal to $52.5$. This set fits your description. See if you can calculate the standard deviation.
Now consider the set that has $25$ elements equal to $2.5$ and $25$ elements equal to $52.5$. This set also fits your description - what's the standard deviation here?