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QJEEM20Ma896e: JEE Main 2020 Mathematics - Class 11 JEEM20Ma896e Solution: The mean and variance of 8 observations are 10 and 13.5,…

The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5, 7, 10, 12, 14, 15, then the absolute difference of the remaining two observations is :

Multiple Choice Options

  • A 5
  • B 3
  • C 7
  • D 9

Step-by-Step Verified Solution

Let the two remaining observations be x and y.

∵ x¯=10=5+7+10+12+14+15+x+y8

⇒x+y=17 ....(1)

∵ var(x)=13.5=25+49+100+144+196+225+x2+y28−(10)2

⇒x2+y2=169 ....(2)

From (1) and (2)

(x, y) = (12, 5) or (5, 12)

So |x−y|=7

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