Accuracy and Error
Model evaluation stands on two pillars. Every metric in the rest of this unit is built out of these two ideas, so it is worth being slow here.
1Bob, Billy and the concert
Bob and Billy went to a concert. Bob brought ₹300 and Billy brought ₹550. The entry fee was actually ₹500 per person.
Who was more accurate, and by how much was each of them out?
Billy: |500 − 550| = 50 out.
Billy is more accurate, because his error is smaller. Notice that Billy guessed over and Bob guessed under, but that does not matter — we take the size of the gap, not its direction.
2The two definitions
Two questions about the same throw
Error asks: when it missed, how far away did it land?
You need both. A player who hits the board half the time but is never far off is a very different player from one who hits half the time and otherwise misses the wall.
3Working it out
For a model that predicts a number — a regression model, like a house price — accuracy is worked out per prediction and then averaged:
| Step | Formula |
|---|---|
| Error | Abs(Actual − Predicted) |
| Error rate | Error / Actual |
| Accuracy | 1 − Error rate |
| Accuracy % | Accuracy × 100 |
| Model accuracy | The mean accuracy of all the samples |
Dividing by the actual value turns the error into a proportion. Being 30k out on a 900k house is a small miss; being 30k out on a 97k house is an enormous one, and only the error rate shows that.
A regression model, so there is no confusion matrix — accuracy here means how close each prediction came.
| Predicted | Actual | Error = |Actual − Predicted| | Error rate = Error / Actual | Accuracy = 1 − rate | Accuracy % |
|---|---|---|---|---|---|
| 391k | 402k | |402k − 391k| = 11k | 11/402 = 0.0274 | 1 − 0.0274 = 0.9726 | 97.3% |
The accuracy of the model is the mean accuracy of all five samples — 86.60% once every row is in. Notice row 3: the model was only 28k out, but on a 97k house that is a much worse miss than being 36k out on a 907k one. That is why the error is divided by the actual value.
4Accuracy is not the whole story
Real-world data is messy, and even the best models make mistakes. Two warnings the handbook gives, both worth remembering:
- Focusing only on accuracy can be a mistake. In medical diagnosis, a model with slightly lower accuracy but a strong focus on not calling a healthy person sick may well be preferable.
- The right metric depends on the task. Choosing which error or accuracy measure to quote is part of the job, not a detail.
5From the board papers
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5. Abs(80 − 75) = 5. The word absolute is why the answer is not −5.
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10%. 10 of the 100 were wrong, so the error rate is 10/100 = 0.1 = 10%. Accuracy and error rate always add up to 100%.
Reason (R): Error helps us evaluate how accurately a model can predict both training and unseen data, which is why it is used to select the best-performing model.CBSE sample paper 2025–26
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Both (A) and (R) are correct, and (R) is the correct explanation of (A). Lower error means better performance precisely because error is the measure we use to compare models and pick one.
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Accuracy tells you how many predictions the model got right, and error tells you how far the wrong ones were from the truth. On their own neither is enough: a model can be accurate most of the time yet be badly wrong when it fails, and two models with the same accuracy can have very different errors. The goal of evaluation is to minimise error and maximise accuracy, so both have to be understood in order to compare models and improve them.
6Check yourself
The goal when evaluating an AI model is to:
A model predicts a house at 391k when it actually sold for 402k. What is the error?
Accuracy and model performance are: