Z-distributions, normal distributions

How can I compare two different datasets or distributions?

The following is the formula for the z-statistic.

$$z = \frac{x - \mu}{\sigma}$$

By performing this operation on each value of x , subtracting it by the mean, then dividing the difference with the standard deviation, you get z which is the normalized value of that datapoint into the normal distribution.

This transformation changes a dataset into a normalized form that is ready for comparison, producing a Normal Distribution.

Why do this?

We want to do this because sometimes we want to compare different datasets (e.g. MBA scores vs. MBAN scores). However, because datasets are different we need to have a "standardized" or "normalized" format that we can compare them.

That normalized format is when a distribution has a mean of 0 and standard deviation is 1.

What is it like?

The mean is 0, the standard deviation is 1. The distributions may look differently though.

By John E Pattison, retrieved at ResearchGate.

All of the above distributions are normal (i.e. mean is zero, standard deviation is 1) but the distributions are different.

Example

To be added soon.