JEE Mathematics · Hard

Statistics: Variance formula MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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Variance formulaHardQuestion 380009

Question

Variance = (Σx²/n) − (x̄)². This formula shows:
  1. A
    Variance = mean of squares − square of mean
    Correct
  2. B
    Variance = mean − standard deviation
  3. C
    Variance = range²
  4. D
    Variance = median²

Correct answer

Variance = mean of squares − square of mean

Explanation

Alternative variance formula: σ² = (Σxᵢ²/n) − (x̄)². This is computationally easier than finding deviations from mean. Derived by expanding Σ(xᵢ−x̄)²/n.