Does standardization make a distribution normal?

Conditions

• The dataset has a well-defined mean and standard deviation.
• Standardization is applied as a linear transformation.

Reasoning, step by step

1. Apply the standardization formula $x' = \frac{x - \bar{x}}{\sigma}$ to the data.
2. Observe that the transformation only involves subtraction and division by constants.
3. Note that these operations shift and scale the data along the x-axis but do not alter the relative heights or shape of the histogram.
4. Conclude that the underlying distribution shape (e.g., skewness) remains unchanged.

Example

The video shows a highly right-skewed blue histogram. After applying standardization, the resulting orange histogram retains its right-skewed shape, demonstrating that it does not become a normal (bell-shaped) distribution.

Common misconceptions

• Believing that standardization transforms any dataset into a normal distribution.
• Assuming that adjusting the mean and standard deviation inherently changes the shape of the data distribution.

Watch the explanation

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