What is the Z-score formula?

Conditions

• Requires knowing the mean and standard deviation of the dataset

Reasoning, step by step

1. Identify the original data value $X$.
2. Calculate or identify the mean $\mu$ of the dataset.
3. Calculate or identify the standard deviation $\sigma$ of the dataset.
4. Substitute these values into the formula $X' = \frac{X - \mu}{\sigma}$ to get the normalized value.

Example

The whiteboard shows X' = (X - mean μ) / Std dev σ. For a student height of 64, with a mean of 70 and standard deviation of 4, the Z-score is $\frac{64 - 70}{4} = -1.5$.

Common misconceptions

• Confusing the Z-score formula with the Min-Max formula, which uses minimum and maximum values instead of mean and standard deviation.

Watch the explanation

Explore next

• How is standard deviation calculated from a set of data values?
• How to standardize a dataset using the Z-score formula?