Can we use a normalized standard deviation to represent a large or small variation when we have data sets with different scales? For example, the first data set has numbers between 1,000,000 and 1,200,000 and the standard deviation is 3000. On the other hand the second data set has numbers between 0 and 200 and the standard deviation is 30.
Comparing these two, we roughly say that the variation in the first data set is smaller than the second data set. I would like to know how can I normalize the std values? Diving by the mean value? Or dividing by the max value? Any suggestion about that?
Best Answer
"Coefficient of variation" is a statistic that seems to get at what you're describing, where you divide the standard deviation by the mean. However, for your task of saying which group has more variability, it seems straightforward: one group has $100$-times as high a standard deviation of the other. Given that one variable is spread over a range of $200$ and the other over a range of $200,000$, this is what I would expect, and I would be comfortable disagreeing with your assessment that the second group is more variable than the first.