Verified Solution • 2025–26 Session moderate

QJEEM21Ma05d8: JEE Main 2021 Mathematics - Class 11 JEEM21Ma05d8 Solution: The mean and variance of 7 observations are 8 and 16…

The mean and variance of 7 observations are 8 and 16 respectively. If two observations are 6 and 8, then the variance of the remaining 5 observations is :

Multiple Choice Options

  • A 925{{92} \over 5}
  • B 1345{{134} \over 5}
  • C 53625{{536} \over {25}}
  • D 1125{{112} \over 5}

Step-by-Step Verified Solution

Let 8, 16, x1, x2, x3, x4, x5 be the observations.

Now, x1+x2+....+x5+147=8{{{x_1} + {x_2} + .... + {x_5} + 14} \over 7} = 8

⇒∑i=15xi=42\Rightarrow \sum\limits_{i = 1}^5 {{x_i} = 42} .... (1)

Also, x12+x22+...x52+82+627−64=16{{x_1^2 + x_2^2 + ...x_5^2 + {8^2} + {6^2}} \over 7} - 64 = 16

⇒∑i=15xi2=560−100=460\Rightarrow \sum\limits_{i = 1}^5 {x_i^2 = 560 - 100 = 460} ..... (2)

So variance of x1, x2, ......., x5

=4605−(425)2=2300−176425=53625= {{460} \over 5} - {\left( {{{42} \over 5}} \right)^2} = {{2300 - 1764} \over {25}} = {{536} \over {25}}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring