After working with MSE and MAE, I came across another important metric:

Mean Absolute Percentage Error (MAPE).

At first, it seemed a bit confusing. The idea of percentages inside a
formula made it feel more complex than the others. But once I started
learning it step by step, everything became much clearer.

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🧠 Starting with the basic idea

I began with a simple example:

–

y = 100, ŷ = 80

Step by step:

–

Difference = |100 – 80| = 20
–

Percentage error = 20 / 100 = 0.2
–

MAPE = 0.2 or 20%

That’s when it clicked:

👉 MAPE measures error in percentage, not just absolute numbers.

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🔢 Practicing with multiple values

Then I tried working with more data:

–

y = [100, 200]
–

ŷ = [90, 220]

Steps:

–

Errors = 0.1 and 0.1
–

Sum = 0.2
–

MAPE = 0.2 / 2 = 0.1 → 10%

By arranging these steps in the correct order, I started to recognize the
pattern.

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📈 Understanding the process

The full method became clear:

1.

Calculate the absolute difference
2.

Divide by the real value
3.

Repeat for all data points
4.

Take the average

Compared to MAE, there’s one extra step:

👉 dividing by the actual value

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📊 Connecting to the formula

Then I looked at the formula:

MAPE = (1/n) × Σ(|y – ŷ| / y)

Now I understood:

–

y = real values
–

ŷ = predictions
–

n = number of values

The formula was just a shortcut for the steps I already knew.

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📉 What MAPE tells us

MAPE gives a very intuitive result:

–

10% → small error
–

20% → moderate error
–

50% → large error

This makes it easy to explain results—even to people without a math
background.

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⚠️ Important insight

While learning, I noticed something important:

👉 Small real values can create large percentage errors

For example:

–

y = 10, ŷ = 5 → error = 50%

That means:

–

MAPE can become unstable with small numbers
–

It needs careful interpretation

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⚖️ Comparing MAPE with MSE and MAE

From my experience:

–

MSE → sensitive to large errors
–

MAE → treats all errors equally
–

MAPE → expresses error in percentages

Each one has its own purpose depending on the situation.

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🎯 Why this method worked for me

–

I used real numbers
–

I followed clear steps
–

I connected formulas to actual meaning
–

I learned actively instead of memorizing

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🚀 Final thoughts

MAPE became much easier once I approached it step by step and practiced
with real examples.