Verified Solution • 2025–26 Session moderate

QJEEM19Ma69df: JEE Main 2019 Mathematics - Class 11 JEEM19Ma69df Solution: The mean of five observations is 5 and their variance is 9.20.…

The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is -

Multiple Choice Options

  • A 6:07
  • B 10:03
  • C 4:09
  • D 5:08

Step-by-Step Verified Solution

Let two observations are x1 & x2

mean = ∑xi5=5

⇒1+3+8+x1+x2=25

⇒x1+x2=13      . . . . (1)

variance (σ2) = ∑xi25−25=9.20

⇒  ∑xi2=171

⇒  x12+x22=97      . . . . . (2)

⇒(x1 + x2)2 − 2x1x2 = 97

⇒ 169 - 2x1x2 = 97

or   x1x2 = 36

∴  x1 : x2 = 4 : 9

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