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JEE Main 2008
Exam
JEE Main
Year
2008
Subject
Mathematics
Chapter
Statistics

JEE Main 2008 · Mathematics · Statistics

The mean of the numbers a, b, 8,5,10 is 6 and the variance is 6.80...

The mean of the numbers a,b,8,5,10a, b, 8,5,10 is 6 and the variance is 6.806.80. Then which one of the following gives possible values of aa and bb ?

Options

  1. Aa=0,b=7a=0, b=7
  2. Ba=5,b=2a=5, b=2
  3. Ca=1,b=6a=1, b=6
  4. Da=3,b=4a=3, b=4

Correct answer

D. a=3,b=4a=3, b=4

Step-by-step solution

Mean of a,b,8,5,10a, b, 8,5,10 is 6 ⇒a+b+8+5+105=6⇒a+b=7\begin{aligned}& \Rightarrow \frac{a+b+8+5+10}{5}=6 \\ & \Rightarrow a+b=7 \end{aligned}Given that Variance is 6.86.8∴ Variance =∑(Xi−A)2n=(a−6)2+(b−6)2+4+1+165=6.8\begin{aligned}& \therefore \text{ Variance }=\frac{\sum\left(\mathrm{X}_{\mathrm{i}}-\mathrm{A}\right)^2}{\mathrm{n}}\\ & =\frac{(\mathrm{a}-6)^2+(\mathrm{b}-6)^2+4+1+16}{5}=6.8 \end{aligned}$\begin{aligned}& \Rightarrow a²+b²=25 \\ & a²+(7-a)^2=25 \\ & \Rightarrow a²-7 a+12=0 \\ & \therefore a=4,3 \text{\text{ and } }b=3,4 \end{aligned}
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