Normalizing and Scaling

Who this is for

Analysts who prepare datasets for modeling or reporting and need consistent feature scales for algorithms (k-NN, k-means, PCA, regressions) and clear dashboards.

Prerequisites

• Comfort with basic stats: mean, median, standard deviation, percentiles.
• Ability to load data in spreadsheets, SQL, or Python/R.
• Know the difference between numeric and categorical features.

Why this matters

Many models and distance-based methods are scale-sensitive. A feature measured in thousands can dominate another in decimals. Proper scaling avoids misleading results and improves training stability. In real tasks, you will:

• Prepare customer metrics for clustering (k-means needs scaled inputs).
• Standardize inputs for logistic/linear regression to stabilize coefficients.
• Normalize ranges for dashboards so indicators plot comparably.

Concept explained simply

Scaling changes the units of a feature without changing its information. Think "resizing" values so features are comparable. Two common ways:

• Normalization (Min–Max scaling): squashes values to a fixed range (usually 0 to 1).
• Standardization (Z-score): centers values around 0 and scales by spread so typical values are around −1 to 1.

Mental model

Imagine different thermometers for the same room: one in °C, another in °F. They show different numbers for the same heat. Scaling is converting them to the same ruler so distances and comparisons make sense.

Key methods

Min–Max scaling (Normalization)

Formula: (x − min) / (max − min) → result in [0,1] if no outliers.

• Great for bounded inputs and algorithms using distances (k-NN, k-means).
• Sensitive to outliers because min/max can be extreme.

Z-score standardization (Standardization)

Formula: (x − mean) / std → mean ≈ 0, std ≈ 1.

• Good default for many linear models and PCA.
• Sensitive to outliers (mean and std move).

Robust scaling

Formula: (x − median) / IQR, where IQR = Q3 − Q1.

• Resistant to outliers; ideal for skewed/heavy-tailed data.
• Values are not bounded; range depends on distribution.

Reliable workflow

1. Profile data: check min, max, mean, std, median, IQR; inspect outliers.
2. Choose scaler per feature group (e.g., robust for skewed revenue, z-score for balanced rates).
3. Fit scaler on training data only; apply same transform to validation/test/production.
4. Save scaler parameters (min/max or mean/std or median/IQR) for reproducibility.
5. Document transformed features and reasons.

Worked examples

Example 1: Min–Max for two features

Data: order_value = [20, 50, 80], items_count = [1, 3, 5].

• order_value: min=20, max=80 → [ (20−20)/60=0, (50−20)/60=0.5, (80−20)/60=1 ] → [0, 0.5, 1]
• items_count: min=1, max=5 → [ (1−1)/4=0, (3−1)/4=0.5, (5−1)/4=1 ] → [0, 0.5, 1]

Example 2: Z-score for a rate

Data: conversion_rate = [0.08, 0.10, 0.12]. mean=0.10, std≈0.01633.

• (0.08−0.10)/0.01633≈−1.225, (0.10−0.10)/0.01633=0, (0.12−0.10)/0.01633≈+1.225

Example 3: Robust scaling for skewed revenue

Data: revenue = [30, 32, 35, 40, 120]. Q1=32, median=35, Q3=40 → IQR=8.

• (30−35)/8=−0.625, (32−35)/8=−0.375, (35−35)/8=0, (40−35)/8=0.625, (120−35)/8=10.625

MinMax: =(A2 - MIN($A$2:$A$100)) / (MAX($A$2:$A$100)-MIN($A$2:$A$100))
Z-score: =(A2 - AVERAGE($A$2:$A$100)) / STDEV.S($A$2:$A$100)
Robust: =(A2 - MEDIAN($A$2:$A$100)) / (QUARTILE.INC($A$2:$A$100,3)-QUARTILE.INC($A$2:$A$100,1))

SELECT x,
       (x - MIN(x) OVER()) / NULLIF(MAX(x) OVER() - MIN(x) OVER(),0) AS x_minmax
FROM t;

from sklearn.preprocessing import MinMaxScaler, StandardScaler, RobustScaler
scaler = RobustScaler()
X_scaled = scaler.fit_transform(X_train)
X_test_scaled = scaler.transform(X_test)

Practical projects

• Customer clustering: scale monetary, frequency, and recency differently (e.g., robust for spend, z-score for frequency).
• Churn model prep: z-score continuous features, keep binaries as-is; compare model stability with/without scaling.
• PCA for dimensionality reduction: standardize features and visualize variance explained.

Exercises

Complete these two exercises. A quick checklist before you start:

• Identify outliers and skewness.
• Pick the right scaler per feature.
• Fit on training data parameters only.
• Verify transformed ranges/means.

Exercise 1: Mixed scaling

Dataset (rows):

order_value: [40, 70, 100, 160]
items_count: [1, 2, 4, 7]
discount_rate: [0.00, 0.05, 0.10, 0.20]

Tasks:

• Min–Max scale order_value and items_count to [0,1].
• Z-score standardize discount_rate.

Exercise 2: Robust scaling on skewed incomes

Data: annual_income_k = [30, 32, 35, 36, 38, 40, 120]

Tasks:

• Compute median, Q1, Q3, IQR.
• Robust scale each income: (x − median) / IQR.

Common mistakes and self-check

• Fitting on full data (leakage): Always fit scaler on training only, then transform validation/test. Self-check: ensure you reuse the same fitted parameters.
• Scaling categorical or binary flags unnecessarily: Usually keep as 0/1. Self-check: list all scaled columns; confirm only continuous features included.
• Ignoring outliers with Min–Max: Leads to compressed ranges. Self-check: compare min/max before and after; inspect 1st/99th percentiles.
• Forgetting to save parameters: Causes inconsistent production transforms. Self-check: export min/max or mean/std or median/IQR alongside model.
• Dividing by zero: Constant columns break scaling. Self-check: drop zero-variance features first.

Learning path

1. Data profiling: distributions, missing values, outliers.
2. Choose scaler per feature type and distribution.
3. Implement transforms in your tool (Excel/SQL/Python/R).
4. Validate with simple models (k-NN or regression) to see impact.
5. Package: persist parameters and document workflow.

Next steps

• Add scaling steps into your standard data-cleaning pipeline template.
• Test different scalers and compare model performance.
• Create a short doc that maps features to chosen scalers and why.

Mini challenge

You have two features: time_on_site_seconds (heavily skewed with few very long sessions) and pages_viewed (0–20, roughly symmetric). Choose a scaler for each and justify in one sentence. Then implement quickly on a 10-row sample.

Quick Test

Take the quick test below to check your understanding. Available to everyone. If you log in, your progress will be saved automatically.