Statistics

MSE Calculator (Mean Squared Error)

Find the mean squared error between predicted and actual values.

Predicted 1

Actual 1

Predicted 2

Actual 2

Predicted 3

Actual 3

Calculated Output

Mean squared error 0.5

Root mean squared error 0.7071

Formula: MSE = mean of (predicted − actual)²

Step-by-Step Breakdown

1. Values used:

2. Predicted 1 = 3

3. Actual 1 = 2.5

4. Predicted 2 = 5

5. Actual 2 = 5.5

6. Predicted 3 = 8

7. Actual 3 = 7

9. Mean squared error = Predicted 1 - Actual 1 = 3 - 2.5 = 0.5

10. Root mean squared error = 0.7071

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The math behind it

MSE = mean of squared errors. RMSE = √MSE puts it back in the original units.

Errors 0.5, −0.5, 1 → MSE 0.5, RMSE ≈ 0.71.

Why square the errors?

It penalizes large errors more and keeps positives and negatives from cancelling.