# How can you normalize two data sets to the same scale?

I have two data sets, one that ranges from 0-200, and another that ranges from ~400-~2500.

I would like to compare the two according to a score from 0-10. I remember about normalizing from a statistics class that I took that in order to normalize you need to find the z-score which depends on the population mean and standard deviation (which I have). But I don't remember what to do with that z-score, or how to normalize both of these data sets down to a 0-10 scale so that they can be scaled down and compared against each other.

Anyone remember how to do this?

• If you have z-scores do you mean that you have both in standard normal form? You could then simply design some scale from 0-10 that depends on z scores – 123 Jan 15 '15 at 18:58
• I'd like to get both distributions in standard normal form. But by z score, I took (random variable - mean)/stddev from the original data set. I'd like to know how to scale it down to standard normal form. – johncorser Jan 15 '15 at 19:00
• The right approach depends on why you want the score to run from $0$ to $10$. If you intend this score to be proportional to a quantile, you'll need $10\Phi(z)$, with $\Phi$ the $N(0,\,1)$ cdf. – J.G. Sep 1 '19 at 17:20

## 1 Answer

The z-score is the standardisation that you should plot. Full-stop. (And you have the correct formula for the z-score.) The z-score might usually range from -3 to +3 and you can then plot both z-score distributions on the same graph. The z-score distributions plot with their centres at z=0. You mention you want to plot on a 0-10 scale. What do you mean by this ?