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Standardising a feature affects its distribution by centering it around zero and scaling its spread.

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While standardisation transforms the mean and variance, it does not alter the shape of the distribution; a bell-shaped curve remains bell-shaped.

Standardisation is critical in algorithms that assume normally distributed data, or when features are on different scales and need to be brought to a common scale.

Example

If we standardise the distribution of shot distances in basketball, the transformed data will still show a normal distribution but centered at zero. This allows a clearer analysis of shot efficiency relative to the average shooting distance.

Next reading:

Handling ‘unbounded’ data