How to normalize data in Python

Data normalization is a key step for preparing datasets for analysis. Python offers powerful tools to scale your data, ensuring model accuracy and consistent performance across different features.

You'll learn several normalization techniques with practical tips. You will also see real-world applications and get advice to debug common issues, helping you choose the right method.

Using simple min-max normalization

import numpy as np

data = np.array([2, 5, 10, 12, 18])

# Min-Max scaling to range [0, 1]
normalized_data = (data - np.min(data)) / (np.max(data) - np.min(data))
print("Original data:", data)
print("Normalized data:", normalized_data)--OUTPUT--Original data: [ 2 5 10 12 18]
Normalized data: [0. 0.1875 0.5 0.625 1. ]

Min-max normalization is a straightforward way to rescale features to a fixed range, typically between 0 and 1. This is especially useful for algorithms that are sensitive to the scale of input data, like gradient descent or K-Nearest Neighbors.

The core logic is in the formula (data - np.min(data)) / (np.max(data) - np.min(data)). Here’s how it works:

• First, data - np.min(data) shifts every value so the dataset's minimum becomes 0.
• Then, dividing by the range—np.max(data) - np.min(data)—scales all values proportionally, mapping the original maximum to 1.

Basic normalization techniques

Beyond the basic min-max approach, you can tailor normalization to your specific needs with a few other powerful yet straightforward methods.

Using min-max scaling with custom range

import numpy as np

data = np.array([2, 5, 10, 12, 18])

# Min-Max scaling to range [-1, 1]
min_val, max_val = np.min(data), np.max(data)
normalized_data = 2 * (data - min_val) / (max_val - min_val) - 1
print("Normalized to [-1, 1]:", normalized_data)--OUTPUT--Normalized to [-1, 1]: [-1. -0.625 0. 0.25 1. ]

You can easily adapt the formula to scale data into a custom range, such as [-1, 1]. This is particularly useful for certain machine learning models. The logic builds directly on the standard [0, 1] scaling by simply stretching and shifting the result.

• The core (data - min_val) / (max_val - min_val) expression first maps your values to the [0, 1] range.
• Multiplying the result by 2 expands this range to [0, 2].
• Subtracting 1 then shifts the entire dataset down to fit the final [-1, 1] range.

Using z-score normalization (standardization)

import numpy as np

data = np.array([2, 5, 10, 12, 18])

# Z-score normalization
normalized_data = (data - np.mean(data)) / np.std(data)
print("Original data:", data)
print("Z-score normalized:", normalized_data)--OUTPUT--Original data: [ 2 5 10 12 18]
Z-score normalized: [-1.30384048 -0.84749831 0.06519218 0.37958772 1.70655889]

Z-score normalization, or standardization, transforms your data to have a mean of 0 and a standard deviation of 1. Unlike min-max scaling, it doesn't bind your data to a specific range, which makes it less sensitive to outliers. The logic is handled by the formula (data - np.mean(data)) / np.std(data).

• The data - np.mean(data) part centers all values around zero.
• Dividing by np.std(data) then scales the data, expressing each value in terms of its distance from the mean in standard deviations.

Using decimal scaling

import numpy as np

data = np.array([200, 500, 1000, 1200, 1800])

# Decimal scaling
j = int(np.ceil(np.log10(np.max(np.abs(data)))))
normalized_data = data / 10**j
print("Original data:", data)
print("Decimal scaled:", normalized_data)--OUTPUT--Original data: [ 200 500 1000 1200 1800]
Decimal scaled: [0.02 0.05 0.1 0.12 0.18]

Decimal scaling normalizes data by moving the decimal point. The goal is to find a power of 10 that's just large enough to scale down every number in your dataset, so the largest absolute value becomes less than 1.

• The key is calculating j, the exponent. The code uses np.log10 on the maximum absolute value to find its number of digits, and np.ceil rounds it up to the next whole number.
• Finally, dividing the entire dataset by 10**j performs the scaling, ensuring all values are mapped into a consistent range.

Advanced normalization techniques

Now that you've seen the basics, you can tackle more complex scenarios with robust methods, dedicated libraries, and even your own custom functions.

Using robust scaling with median and IQR

import numpy as np

data = np.array([2, 5, 10, 12, 18, 100]) # With outlier

# Robust scaling using median and IQR
median = np.median(data)
q1, q3 = np.percentile(data, [25, 75])
iqr = q3 - q1
robust_scaled = (data - median) / iqr
print("Original data:", data)
print("Robust scaled:", robust_scaled)--OUTPUT--Original data: [ 2 5 10 12 18 100]
Robust scaled: [-0.71428571 -0.35714286 0. 0.14285714 0.57142857 6.42857143]

Robust scaling is your go-to method when your data contains outliers, like the value 100 in the example. Unlike the mean, the median isn't easily skewed by extreme values. This approach centers your data and scales it based on the spread of the middle portion of your dataset, making it more resilient.

• First, the formula subtracts the median from each data point to center the distribution.
• Then, it divides the result by the Interquartile Range (iqr)—the range between the 25th and 75th percentiles—which scales the data based on its central bulk.

Using scikit-learn preprocessing modules

import numpy as np
from sklearn.preprocessing import MinMaxScaler, StandardScaler

data = np.array([[2, 200], [5, 500], [10, 1000], [12, 1200], [18, 1800]])

mm_scaler = MinMaxScaler()
std_scaler = StandardScaler()
print("MinMax scaled:\n", mm_scaler.fit_transform(data))
print("Standard scaled:\n", std_scaler.fit_transform(data))--OUTPUT--MinMax scaled:
[[0. 0. ]
[0.1875 0.1875 ]
[0.5 0.5 ]
[0.625 0.625 ]
[1. 1. ]]
Standard scaled:
[[-1.30384048 -1.30384048]
[-0.84749831 -0.84749831]
[ 0.06519218 0.06519218]
[ 0.37958772 0.37958772]
[ 1.70655889 1.70655889]]

For real-world projects, you'll often use libraries like scikit-learn. Its preprocessing module offers optimized tools like MinMaxScaler and StandardScaler that handle the math for you. This is far more efficient than writing normalization logic from scratch, especially with multi-column datasets.

• The fit_transform() method is a convenient shortcut. It first learns the scaling parameters from your data—the “fit” part—and then applies the transformation in one step.
• These scalers automatically process each column of your data independently, ensuring consistent scaling across your entire dataset.

Creating custom normalization with mathematical functions

import numpy as np

def normalize_with_function(data, func=np.tanh):
return func(data / np.max(data))

data = np.array([2, 5, 10, 12, 18])
tanh_normalized = normalize_with_function(data)
sigmoid_normalized = normalize_with_function(data, lambda x: 1/(1+np.exp(-x)))
print("Tanh normalized:", tanh_normalized)
print("Sigmoid normalized:", sigmoid_normalized)--OUTPUT--Tanh normalized: [0.10991413 0.2673152 0.49757422 0.56456214 0.74222773]
Sigmoid normalized: [0.57444252 0.64565631 0.73105858 0.76159416 0.84553473]

You can create your own normalization logic by wrapping mathematical functions in a custom Python function. The normalize_with_function example accepts any function, like np.tanh or a custom lambda, to transform your data. This gives you the flexibility to apply non-linear transformations tailored to your specific needs.

• The data is first scaled by dividing each value by the dataset's maximum using data / np.max(data).
• Then, a mathematical function like tanh or sigmoid is applied to these scaled values.
• This approach is great for tasks where you need to squash values into a specific range, such as preparing inputs for a neural network.

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For the normalization techniques we've explored, Replit Agent can turn them into practical applications:

• Build a data preprocessing utility that lets users apply methods like MinMaxScaler or robust scaling to their own datasets.
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Common errors and challenges

Even with powerful tools, you can run into a few common pitfalls when normalizing data in Python.

Handling division by zero in min-max normalization

A DivisionByZeroError can pop up during min-max normalization if all the values in your dataset are identical. When this happens, the minimum and maximum values are the same, making the denominator in the formula—max(data) - min(data)—equal to zero. This is a classic case where the math just doesn't work.

• To prevent this, you should add a simple check before you normalize. If the range is zero, you can decide how to proceed. Often, the best approach is to return an array of zeros, since there's no variation to scale.

Fixing NaN values in z-score normalization

Similarly, you might see NaN (Not a Number) values appear after applying z-score normalization. This happens for the same reason as the division-by-zero error: your dataset contains constant values. A constant dataset has a standard deviation of zero, and dividing by zero in the z-score formula results in NaN.

• The fix is to check if the standard deviation is zero before you divide. If it is, you can again return an array of zeros, as every value is exactly at the mean with no deviation.

Handling missing values before normalization

Most normalization functions will fail or produce unexpected results if your data contains missing values, often represented as NaN. These values can corrupt calculations for the mean, median, or standard deviation, which in turn poisons your entire normalized output. It's crucial to handle them before you attempt to scale your data.

• You have a few options. You can use imputation to replace missing values with the column's mean, median, or mode. Alternatively, you could simply remove any rows or columns that contain missing data, though this might lead to information loss.

Handling division by zero in min-max normalization

When all values in your dataset are identical, min-max normalization fails. The denominator in the formula, np.max(data) - np.min(data), becomes zero, leading to a DivisionByZeroError. See what happens when you run the code on such a dataset.

import numpy as np

# All values are the same
data = np.array([5, 5, 5, 5, 5])
# This will cause division by zero
normalized_data = (data - np.min(data)) / (np.max(data) - np.min(data))
print(normalized_data)

Since every element in the array is 5, both np.min(data) and np.max(data) return the same value. The subtraction results in zero, causing a division error. The code below shows how to prevent this.

import numpy as np

data = np.array([5, 5, 5, 5, 5])
# Check if max equals min to avoid division by zero
if np.max(data) == np.min(data):
normalized_data = np.zeros_like(data)
else:
normalized_data = (data - np.min(data)) / (np.max(data) - np.min(data))
print(normalized_data)

The fix is to check for a zero-range scenario before normalizing. The code uses an if statement to test if np.max(data) equals np.min(data). If they’re the same, it returns an array of zeros with np.zeros_like(data), since there's no variation to scale. Otherwise, it performs the calculation as usual. This is a crucial safeguard when working with datasets that might contain constant features, preventing your code from crashing unexpectedly.

Fixing NaN values in z-score normalization

Just like with min-max scaling, z-score normalization runs into trouble with constant data. Because the standard deviation becomes zero, any attempt to divide by it results in NaN values across your array. The code below shows this error in action.

import numpy as np

# All values are identical
data = np.array([10, 10, 10, 10])
# Standard deviation is zero, leading to NaN values
normalized_data = (data - np.mean(data)) / np.std(data)
print(normalized_data)

Since every value is identical to the mean, the numerator becomes zero. The standard deviation is also zero, leading to a 0/0 calculation that results in NaN. The following code shows how to safeguard your function against this.

import numpy as np

data = np.array([10, 10, 10, 10])
# Check if std is zero to avoid NaN values
std = np.std(data)
if std == 0:
normalized_data = np.zeros_like(data)
else:
normalized_data = (data - np.mean(data)) / std
print(normalized_data)

The fix is to check the standard deviation before you normalize. If np.std(data) is zero, it means all your data points are identical. Since you can't calculate a meaningful z-score, the code returns an array of zeros using np.zeros_like(data). This simple if check prevents NaN errors and keeps your script running smoothly. It's a crucial safeguard when processing datasets where some features might not have any variation.

Handling missing values before normalization

Normalization functions will fail if your data contains missing values, often represented as np.nan. Because any mathematical operation involving np.nan returns NaN, the entire calculation breaks down and corrupts your output. The code below shows this problem in action.

import numpy as np

# Data with missing values
data = np.array([2, 5, np.nan, 12, 18])
# This will result in NaN for all values
normalized_data = (data - np.min(data)) / (np.max(data) - np.min(data))
print(normalized_data)

The np.min() and np.max() functions return NaN because the input array contains a missing value. This propagates NaN throughout the entire calculation, corrupting the output. The following code demonstrates how to handle this scenario properly.

import numpy as np

# Data with missing values
data = np.array([2, 5, np.nan, 12, 18])
# Fill missing values with mean before normalizing
mean_value = np.nanmean(data)
clean_data = np.nan_to_num(data, nan=mean_value)
normalized_data = (clean_data - np.min(clean_data)) / (np.max(clean_data) - np.min(clean_data))
print(normalized_data)

The fix is to handle missing values before normalizing. The code first calculates the mean while ignoring NaNs using np.nanmean(). Then, it replaces the np.nan with this mean value using np.nan_to_num(). This process, called imputation, cleans your data so that normalization functions can work correctly. It's crucial to check for missing values before scaling, especially when working with real-world datasets which are often incomplete.

Real-world applications

Beyond troubleshooting, normalization is essential for getting accurate results in fields from computer vision to financial forecasting.

Normalizing image data for CNN models

In computer vision, normalizing pixel values is a critical preprocessing step that ensures your model trains efficiently and converges faster.

import numpy as np
from PIL import Image

# Simulating a grayscale image (like MNIST digit)
image_array = np.random.randint(0, 256, size=(28, 28))

# Normalize pixel values to [0,1] range for neural networks
normalized_image = image_array / 255.0

print(f"Original image shape: {image_array.shape}")
print(f"Original value range: [{np.min(image_array)}, {np.max(image_array)}]")
print(f"Normalized value range: [{np.min(normalized_image):.1f}, {np.max(normalized_image):.1f}]")

This code simulates a grayscale image by creating a 28x28 NumPy array, image_array, with random integer values from 0 to 255. This represents the standard pixel intensity range for an 8-bit image.

The normalization happens when the entire array is divided by 255.0. This simple operation effectively scales all pixel values to a new range between 0.0 and 1.0.

• The lowest possible value, 0, becomes 0.0.
• The highest possible value, 255, becomes 1.0.

This ensures all pixel data is represented consistently as floating-point numbers.

Normalizing financial data for time series analysis

In time series analysis, normalizing financial data is essential for comparing assets, like stocks, that trade in vastly different price ranges.

import numpy as np
import pandas as pd

# Sample stock price data (simulated)
dates = pd.date_range(start='2022-01-01', periods=10, freq='D')
stock_prices = pd.Series([150.5, 152.3, 151.1, 153.7, 158.2,
157.3, 155.6, 160.1, 162.5, 159.8], index=dates)

# Apply min-max normalization for comparing multiple stocks
normalized_prices = (stock_prices - stock_prices.min()) / (stock_prices.max() - stock_prices.min())

print("Original stock prices:")
print(stock_prices.head(3))
print("\nNormalized stock prices (0-1 scale):")
print(normalized_prices.head(3))

This code uses a pandas Series to represent simulated daily stock prices. It then applies min-max normalization to rescale the data into a consistent range between 0 and 1. It’s a common technique for preparing time-series data for machine learning models.

• First, it finds the lowest price in the series and subtracts it from every data point. This shifts the entire dataset so the minimum value is now zero.
• Then, it divides these new values by the total price range (stock_prices.max() - stock_prices.min()), scaling the highest price to 1.

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