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JEE Main 201815 AprilEvening ShiftOnline
Exam
JEE Main
Year
2018
Date
15 April
Shift
Evening Shift
Mode
Online
Subject
Mathematics
Chapter
Statistics

JEE Main 2018 · 15 April · Evening Shift · Online · Mathematics · Statistics

If the mean of the data: 7,8,9,7,8,7, λ, 8 is 8 , then the variance...

If the mean of the data: 7,8,9,7,8,7,λ,87,8,9,7,8,7, \lambda, 8 is 8 , then the variance of this data is

Options

  1. A98\frac{9}{8}
  2. B2
  3. C78\frac{7}{8}
  4. D1

Correct answer

D. 1

Step-by-step solution

xˉ=7+8+9+7+8+7+λ+88=8⇒54+λ8=8⇒λ=10\begin{aligned}&\bar{x}=\frac{7+8+9+7+8+7+\lambda+8}{8}=8 \\ &\Rightarrow \frac{54+\lambda}{8}=8 \Rightarrow \lambda=10 \end{aligned}Now variance =σ2=\sigma^2(7−8)2+(8−8)2+(9−8)2+(7−8)2+(8−8)2=+(7−8)2+(10−8)2+(8−8)28⇒σ2=1+0+1+1+0+1+4+08=88=1\begin{aligned}&(7-8)^2+(8-8)^2+(9-8)^2+(7-8)^2+(8-8)^2 \\ &=\frac{+(7-8)^2+(10-8)^2+(8-8)^2}{8}\\ &\Rightarrow \sigma^2=\frac{1+0+1+1+0+1+4+0}{8}=\frac{8}{8}=1 \\ & \end{aligned}$ Hence, the variance is 1 .
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