Question

How do z scores work?

Answer 1

Z scores are standardized statistics that can be used in a normal distribution with mean 0 and standard deviation 1.

Explanation:

Whenever you obtain sets of data that have a normal distribution that you want to compare, if the sets of data have different means and different standard deviations, it's a bit challenging to make meaningful comparisons. To solve this problem, one can use the z score formula: `(bar x - mu)/sigma`. When you use a value from the original data to create a z score, you basically turned that data value from the original normal distribution to a data value in a normal distribution with a mean of 0 and standard deviation of 1.

Since this formula works for every data set with a normal distribution, it makes for easier comparisons between data sets. For example, if you are looking at a set of test scores for one and a set of test scores for another, you might try looking at the highest score and how much that score deviates from the mean. You could find the z scores for the highest score from each data set and the higher the z score, the more that score deviates from the mean.