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Statistics question

2025 · 29 Jan · Shift 1 · Q38
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  5. /2025 · 29 Jan · Shift 1 · Q38

Statistics question

2025 · 29 Jan · Shift 1 · Q38

JEE MainMathematicsStatisticsMCQ+4 / −1
Let x1,x2,...,x10x_1, x_2, ..., x_{10}x1​,x2​,...,x10​ be ten observations such that ∑i=110(xi−2)=30\sum\limits_{i=1}^{10} (x_i - 2) = 30i=1∑10​(xi​−2)=30, ∑i=110(xi−β)2=98\sum\limits_{i=1}^{10} (x_i - \beta)^2 = 98i=1∑10​(xi​−β)2=98, β>2\beta \gt 2β>2, and their variance is 45\frac{4}{5}54​. If μ\muμ and σ2\sigma^2σ2 are respectively the mean and the variance of 2(x1−1)+4β,2(x2−1)+4β,...,2(x10−1)+4β2(x_1 - 1) + 4\beta, 2(x_2 - 1) + 4\beta, ..., 2(x_{10} - 1) + 4\beta2(x1​−1)+4β,2(x2​−1)+4β,...,2(x10​−1)+4β, then βμσ2\frac{\beta\mu}{\sigma^2}σ2βμ​ is equal to :
  1. A
    100
  2. B
    90
  3. C
    120
  4. D
    110
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