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JEE Main 20244 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
4 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Statistics

JEE Main 2024 · 4 April · Morning Shift · Mathematics · Statistics

Let α, β ∈ R . Let the mean and the variance of 6 observations...

Let α,β∈R\alpha, \beta \in \mathbf{R}. Let the mean and the variance of 6 observations −3,4,7,−6,α,β-3,4,7,-6, \alpha, \beta be 2 and 23 , respectively. The mean deviation about the mean of these 6 observations is :

Options

  1. A133\frac{13}{3}
  2. B163\frac{16}{3}
  3. C113\frac{11}{3}
  4. D143\frac{14}{3}

Correct answer

A. 133\frac{13}{3}

Step-by-step solution

∑xi6=2 and  ∑xi2N−μ2=23α+β=10α2+β2=52\begin{aligned} & \frac{\sum x_i}{6}=2 \text{\text{ and } } \frac{\sum x_i^2}{N}-\mu^2=23 \\ & \alpha+\beta=10 \\ & \alpha^2+\beta^2=52 \end{aligned} solving we get α=4,β=6∑∣xi−xˉ∣6=5+2+5+8+2+46=133\alpha=4, \beta=6 \frac{\sum\left|x_i-\bar{x}\right|}{6}=\frac{5+2+5+8+2+4}{6}=\frac{13}{3}
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