MAE

MAE

English translation by SOTA – AI Community of the Russian original. Organisers who would like this translation removed can email [email protected].

All-Russian School Olympiad in Informatics 2025–2026, Regional Stage, Grades 9–11
“Artificial Intelligence” profile, Tour 1, 17 January 2026
Task D

Points for the task: 50
Answer submission format: entering the answer
Number of attempts: 10
Submission that counts: the last one

Statement

There is a sample of $N = 14$ observations (shown in the figure). Each point is given by a pair of coordinates $(x_i, y_i)$.

Consider the linear prediction $\hat{y}(x) = a \cdot x + b$. Find the minimum

$$MAE = \frac{1}{N} \sum_{i=1}^{N} |\hat{y}(x_i) - y_i|$$

of this prediction on the sample $(x_i, y_i)$ over all $a, b$.

Translator's note: the figure above is the copy published with the official editorial; it is the same image as in the original statement. Read from its grid, the 14 points are $(0, 0)$, $(0, 2)$, $(0, 7)$, $(0, 8)$, $(4, 4)$, $(4, 7)$, $(6, 1)$, $(6, 5)$, $(9, 0)$, $(9, 1)$, $(9, 4)$, $(9, 7)$, $(11, 2)$ and $(11, 6)$.

Output format

Round the answer to 6 decimal places, using a point as the decimal separator.

Scoring

An exact match of the answer: 50 points.

Test results are not available during the tour.