How to Standardize a List with Z-Score Normalization in Python

This code computes the z-score for each number in a list, standardizing the data to have zero mean and unit variance using the statistics module.

Easy Python 3.9+ Aug 9, 2026 Lists & loops 14 views 0 copies

z-score standardization statistics normalization lists

Python code

22 lines

Python 3.9+

import statistics

def z_score_normalize(values):
    """Standardize a list of numbers using z-score normalization."""
    if not values or len(values) < 2:
        raise ValueError("Need at least 2 values for meaningful z-score normalization")
    
    mean = statistics.mean(values)
    std_dev = statistics.stdev(values)  # sample standard deviation
    
    return [(x - mean) / std_dev for x in values]

if __name__ == "__main__":
    data = [2, 4, 6, 8, 10]
    normalized = z_score_normalize(data)
    
    print(f"Original data: {data}")
    print(f"Mean: {statistics.mean(data):.2f}")
    print(f"Std dev: {statistics.stdev(data):.2f}")
    print(f"Z-score normalized: {[f'{x:.2f}' for x in normalized]}")
    print(f"Normalized mean: {statistics.mean(normalized):.2f}")
    print(f"Normalized std dev: {statistics.stdev(normalized):.2f}")

Output

stdout

Original data: [2, 4, 6, 8, 10]
Mean: 6.00
Std dev: 3.16
Z-score normalized: ['-1.26', '-0.63', '0.00', '0.63', '1.26']
Normalized mean: 0.00
Normalized std dev: 1.00

How it works

The statistics.stdev function computes the sample standard deviation (using n-1 degrees of freedom), which is standard for normalizing a sample. The list comprehension [(x - mean) / std_dev for x in values] applies the z-score formula to each element, producing a new list where the mean becomes 0 and the standard deviation becomes 1. This transformation preserves the shape of the distribution while making it comparable across different datasets. The function raises a ValueError if the list has fewer than two elements, because sample standard deviation is undefined for a single value.

Common mistakes

Using `statistics.pstdev` (population standard deviation) instead of `stdev` when the data is a sample, which gives slightly different normalization.
Forgetting to handle empty or single-element lists, causing a `StatisticsError`.
Dividing by zero if the standard deviation is 0 (e.g., all values identical).
Modifying the original list in place instead of returning a new normalized list.

Variations

Use `statistics.pstdev` if the list represents an entire population rather than a sample.
Use a library like NumPy with `(data - np.mean(data)) / np.std(data)` for large datasets and faster computation.

Real-world use cases

Preprocessing features for machine learning models to ensure each input feature has similar scale.
Comparing test scores from different exam versions by converting raw scores to a common scale.
Detecting outliers in sensor data by flagging readings with z-scores exceeding a threshold.

How to Standardize a List with Z-Score Normalization in Python

Python code

Output

How it works

Common mistakes

Variations

Real-world use cases

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