# What is a good type of transformation to try on this data to get normal distribution?

I've tried a log-transformation but data becomes left-skewed.

In general, when data is distributed like this, what is the next best transformation to try if you want to normalize the data?

• Please explain why you need to transform this dataset to look Normal. (Such efforts are usually unnecessary.)
– whuber
Apr 8, 2022 at 20:26
• Computing the inverse of the normal CDF (cumulative distribution function) on the given data might give you close-to-normal distribution. The reason is that your distribution looks a little bit like a uniform distribution in [0,1]. In fact, if this were the case and if we call u a value measured in your distribution and set x = F^-1(u), where F(.) is the standard normal CDF, we have: Pr(X <= F^-1(u)) = Pr(F(X) <= u) = u = F(x), because U has been assumed to be uniform. In R you can get the inverse of the standard normal CDF of u by running qnorm(u). Apr 11, 2022 at 14:50
• @mastropi thank you. makes total sense and it worked. Apr 11, 2022 at 15:56
• "Scaling" and "transforming to normality" are completely different operations.
– whuber
Apr 11, 2022 at 16:31
• @whuber maybe i did (or didn't) phrase this right, but for clustering isn't one of the ways to make variables comparable, which im lead to belive is a necessary step in clustering, to normalize numeric variables? Apr 11, 2022 at 16:47