Z-Score Standardization

Say you scored 90 on a hard test where the average was 70, and also 90 on an easy test where the average was 85. Which 90 is more impressive? Raw scores cannot tell you, but z-scores can. A z-score answers one question: how many standard deviations away from the average is this value? A z-score of 0 means exactly average. A z-score of +2 means solidly above average. A z-score of -1 means a bit below average. Once you turn every value into a z-score, you can fairly compare numbers that come from completely different scales.

1. 1Find the mean and the standard deviation of the whole dataset.
2. 2For each value, subtract the mean. This tells you how far it is from average, in the original units.
3. 3Divide that difference by the standard deviation. This rescales the distance into 'number of standard deviations', which is the z-score.

Use z-scores whenever you need to compare values from different scales or different distributions, like comparing a student's math score to their reading score, or flagging unusually large transactions in fraud detection. This is also a common step before feeding data into models that expect roughly centered, evenly-scaled features.

• ⚠Do not compute the mean and standard deviation on the wrong dataset. Always compute them from the training data, then reuse those same two numbers to standardize the test data.
• ⚠Do not mix up z-score standardization (mean 0, spread measured in standard deviations) with min-max normalization (a fixed 0-to-1 range). They solve a similar problem in different ways.