Welcome to scaling numeric features! Imagine comparing heights in meters versus millimeters - same data, but vastly different numbers.

Machine learning models can get confused when features have different scales, leading to poor predictions.

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Can you name another pair of features you've seen with very different numeric ranges?

Here's the problem: models often calculate distances between data points. A feature with large numbers (like income) will dominate features with small numbers (like age).

It's like shouting over whispers - the loud feature drowns out the quiet ones!

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Which difference will influence distance more—$1 k in income or 1 year in age?

Scaling transforms all features to similar ranges so they contribute equally. There are two main approaches: min-max scaling and standardization.

Min-max scaling squeezes all values into a 0-1 range. Standardization centers values around zero with consistent spread.

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Do any of these approaches sound familiar?

Min-max scaling uses this formula: (value - minimum) ÷ (maximum - minimum)

Let's say we have car ages: 2, 5, 8 years. Minimum = 2, Maximum = 8.

For age 5: (5 - 2) ÷ (8 - 2) = 3 ÷ 6 = 0.5

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What would age 2 become after min-max scaling?

Let's complete our car age example:

• Age 2: (2-2) ÷ (8-2) = 0 ÷ 6 = 0
• Age 5: (5-2) ÷ (8-2) = 3 ÷ 6 = 0.5
• Age 8: (8-2) ÷ (8-2) = 6 ÷ 6 = 1

Notice how all values now fall between 0 and 1?

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Why does the oldest car scale to 1 and the youngest to 0?

You can scale an entire array at once using NumPy:

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Notice how all the values are now between 0 and 1, just like when we did it by hand?

Standardization uses: (value - mean) ÷ standard deviation

Same car ages: 2, 5, 8. Mean = 5, Standard deviation ≈ 2.45.

For age 5: (5 - 5) ÷ 2.45 = 0 ÷ 2.45 = 0

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This centers the average value at zero. What would age 8 become?

Let's complete our car age example using standardization:

• Age 2: (2 - 5) ÷ 2.45 = (-3) ÷ 2.45 ≈ -1.22
• Age 5: (5 - 5) ÷ 2.45 = 0 ÷ 2.45 = 0
• Age 8: (8 - 5) ÷ 2.45 = 3 ÷ 2.45 ≈ 1.22

Now, the average car age is 0, younger cars are negative, and older cars are positive.

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Why do you think standardization can help when features have very different spreads or outliers?

You can also standardize an entire array at once using NumPy:

Now, the average value is 0, and the spread is consistent across the array!

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Does this make sense?

Use min-max scaling when you want values bounded between 0 and 1. It's great for neural networks and when you know the expected range.

Use standardization when your data has outliers or follows a normal distribution. It's preferred for many algorithms.

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Which would work better for test scores ranging 0-100?

Type

Multiple Choice

Practice Question

Let's practice min-max scaling! Scale these house prices to 0-1 range: $100,000, $150,000, $200,000.

What's the scaled value for $150,000?

Formula: (value - min) ÷ (max - min)

A. 0.25 B. 0.5 C. 0.75 D. 1.0

Suggested Answers

• A
• B - Correct
• C
• D