How to standardize a dataset using the Z-score formula?

Conditions

• Requires knowing the mean and standard deviation of the dataset

Reasoning, step by step

1. Calculate the mean $\mu$ by summing all data values and dividing by the total number of values.
2. Calculate the standard deviation $\sigma$ by finding the squared differences from the mean, averaging them, and taking the square root.
3. Substitute each original value $X$, the mean $\mu$, and the standard deviation $\sigma$ into the Z-score formula $X' = \frac{X - \mu}{\sigma}$.
4. Compute the result to get the standardized value $X'$.

Example

For a student height of 64, with a mean of 70 and standard deviation of 4, the Z-score is calculated as $\frac{64 - 70}{4} = \frac{-6}{4} = -1.5$.

Common misconceptions

• Assuming that standardization changes the shape of the data distribution; Z-score standardization only shifts and scales the data, preserving the original distribution shape.

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Explore next

• Why is data normalization necessary in machine learning?
• What is the Z-score formula?