After learning about MSE, I came across another important concept in data
analysis: Mean Absolute Error (MAE). At first, it looked simpler—but I
still didn’t fully understand how it worked or how it was different from
MSE.

What helped me the most was learning MAE through step-by-step ordering and
real calculations.

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🧠 Starting with the basic idea

I began with a simple example:

–

y = 2, ŷ = 5

Step by step:

–

Difference = |2 – 5| = 3
–

Error = 3
–

MAE = 3

The key difference I noticed immediately:

👉 MAE uses the absolute value, not the square.

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🔢 Practicing with multiple values

Next, I tried a slightly bigger example:

–

y = [2, 4]
–

ŷ = [5, 1]

Steps:

–

Differences = 3 and 3
–

Sum = 6
–

MAE = 6 / 2 = 3

By arranging these steps in the correct order, I started to understand the
full process.

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📈 Understanding the general method

With more data points, the process became clear:

1.

Calculate the difference between real and predicted values
2.

Take the absolute value
3.

Add all errors
4.

Divide by the number of values

At this point, I didn’t need to memorize anything anymore—it just made
sense.

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📊 Connecting to the formula

Then I looked at the formula:

MAE = (1/n) × Σ|y – ŷ|

Now I understood every part:

–

y = real values
–

ŷ = predictions
–

n = number of data points

The formula was just a short version of the steps I already knew.

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📉 Interpreting MAE

The most interesting part was understanding what MAE tells us:

–

A smaller MAE means better predictions
–

All errors are treated equally
–

Large errors do not dominate the result

This is very different from MSE.

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⚖️ MAE vs MSE (my insight)

While learning both, I realized:

–

MSE punishes large errors more (because of squaring)
–

MAE treats all errors equally

That means:

–

MAE is more stable
–

MSE is more sensitive

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🎯 Why this method worked for me

–

I learned with real numbers
–

I followed clear steps
–

I understood both calculation and meaning
–

It felt like solving a logical puzzle

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🚀 Final thoughts

MAE became much easier once I focused on step-by-step reasoning instead of
memorizing formulas.