Consider 10 observations x₁, x₂,, x₁₀ such that Σ i=1 ¹⁰(x i -α)=2 and Σ i=1 ¹⁰(x i -β)²=40, where α, β are positive integers. Let the mean and the variance of the observations be 6/5 and 84/25 respectively. Then (β)/(α) is equal to:

Statistics and Probability: JEE Main 2024 Mathematics question

JEE Main 2024 · 1 Feb, Evening shift · Q5489

JEE Main 20241 Feb, Evening shiftMathematicsHardStatistics and Probability258× since 2002

Consider 10 observations

x_1, x_2, \ldots, x_{10}

such that

\sum\limits_{i=1}^{10}\left(x_i-\alpha\right)=2

and

\sum\limits_{i=1}^{10}\left(x_i-\beta\right)^2=40

, where

\alpha, \beta

are positive integers. Let the mean and the variance of the observations be

\frac{6}{5}

and

\frac{84}{25}

respectively. Then

\frac{\beta}{\alpha}

is equal to :