JEE Main 2024 Mathematics question
Let a₁, a₂, ... a₁₀ be 10 observations such that and . Then the standard deviation of a₁, a₂, ..., a₁₀ is equal to:
Answer: (D)
Solution
(Σaₖ)² = Σaₖ² + 2Σ_{k<j} aₖaⱼ, so 2500 = Σaₖ² + 2200 and Σaₖ² = 300. σ = √(300/10 − (50/10)²) = √(30 − 25) = √5.