2016 · Q95
The mean and standard deviation of a set of 16 non- zero positive numbers in an observation are 26 and 3.5 respectively. The mean and standard deviation of another set of 24 non-zero positive numbers without changing the circumstances, are 29 and 3, respectively. The mean and standard deviation of their combined set of observations will respectively be
General Mental Ability, Quantitative Aptitude and StatisticsElementary statistics
- A27.8 and 3.21
- B26.2 and 3.32
- C27.8 and 3.32
- D26.2 and 3.21
Explanation
Combined mean = (16 × 26 + 24 × 29)/40 = 1112/40 = 27.8. The examination uses the pooled-variance convention σ = √[(n1σ1² + n2σ2²)/(n1+n2)] = √[(16×12.25 + 24×9)/40] = √10.3 ≈ 3.21. Hence 27.8 and 3.21 — option (A). (A fully rigorous combined SD including the between-group mean shift would be ≈3.53; the key follows the textbook pooled formula.)