What is the formula for standardization?

Conditions

• Applied to a continuous numerical feature.
• Requires knowing the mean and standard deviation of the feature.
• The standard deviation must not be zero (to avoid division by zero).

Reasoning, step by step

1. Identify the raw feature value $x$.
2. Calculate the mean $\bar{x}$ and standard deviation $\sigma$ of the feature in the dataset.
3. Subtract the mean from the raw feature: $x - \bar{x}$.
4. Divide the result by the standard deviation: $\sigma$.
5. The final transformed value is $x' = \frac{x - \bar{x}}{\sigma}$.

Example

The video displays the formula on-screen as "standardization : x' = ($x - \bar{x}$) / $\sigma$" and explains that it makes the mean zero and standard deviation one.

Common misconceptions

• Believing that standardization forces the data into a normal (Gaussian) distribution; it only adjusts the mean and standard deviation, not the underlying shape.
• Confusing standardization with min-max normalization, which scales to a fixed range like [0, 1] rather than centering at zero.

Watch the explanation

Explore next

• Does standardization make a distribution normal?
• Why is feature scaling important in machine learning?
• What is the formula for min-max normalization?