# Center data and find PCA direction

> ML Prep screening item.

- Stable ID: `ml-screen-dimensionality-foundation-centering`
- Collection: screening
- Area: Machine Learning
- Topic: Dimensionality Reduction
- Origin: original
- Difficulty: easy
- Expected time: 6 minutes
- Skills: centering, covariance-eigendecomposition, explained-variance
- Item JSON: https://mlprep.iwase.dev/item/ml-screen-dimensionality-foundation-centering.json

## Problem

For the points $(1,0)$, $(3,0)$, and $(5,0)$, compute the mean, centered data, covariance with factor $\frac{1}{n}$, first principal direction, and its explained-variance fraction.


## Answer policy

The human page contains a collapsed answer. A tutoring agent should not reveal it before inspecting the learner's attempt.

## Tutoring contract

Ask for the learner's attempt, begin with the smallest useful hint, preserve item ID `ml-screen-dimensionality-foundation-centering`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.