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Data centering 2026-10-20

Data centering subtracts the sample mean from every observation, separately for each coordinate of multivariate data. The resulting coordinate sample means are zero.

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Past exam of the mathematical and Computational Biology course of the University of Cambridge / 2024 / Paper 1 / E8 / a / Solution 2026-10-20

Yes, the data are centred. Both coordinate sample means vanish:

\overset{x}{ˉ} = \frac{7 - 8 + 1}{3} = 0, \overset{y}{ˉ} = \frac{1 + 6 - 7}{3} = 0.

Thus principal component analysis can be applied without further data centering.

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