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Statistics for finance · level 2

Variance the fast way

Never chase deviations one by one. Average the squares, subtract the square of the average — that is the variance, and its root is σ.

Theory: Describing Data

Worked example: Population σ of 2, 4, 4, 6?

mean4
mean of squares18
variance2
σ1.41

Step by step

  1. 1

    Mean

    (2 + 4 + 4 + 6) / 4 = 4

  2. 2

    Mean of the squares

    (4 + 16 + 16 + 36) / 4 = 18

  3. 3

    Variance = mean of squares − square of the mean

    18 − 16 = 2

  4. 4

    σ is the square root

    √2 ≈ 1.41

Population σ of 2, 4, 4, 6? = 1.41

The theory behind it

Intuition

Variance is the mean of squares minus the square of the mean, which is why one pass through the data is enough.

Common pitfalls

  • ×Dividing by n when the sample formula needs n − 1.
  • ×Reporting variance where the question wants standard deviation.

In the interview

Any spread or volatility question.