2026 · Q97
If the mean of 15 observations, namely x₁, x₂, x₃, ..., x₁₅ is 2.5, then what is the value of Σ(i=1 to 15)[5(4xᵢ + 1)]?
Elementary MathematicsStatistics
- A400
- B525
- C625
- D825
Explanation
Expand the sum: Σ 5(4xᵢ + 1) = 20Σxᵢ + 5·15. Since the mean of the 15 observations is 2.5, Σxᵢ = 15·2.5 = 37.5. Substituting gives 20·37.5 + 75 = 750 + 75 = 825, option D.