Verified Solution • 2025–26 Session moderate

QJEEM22Mae374: JEE Main 2022 Mathematics - Class 11 JEEM22Mae374 Solution: The mean of the numbers a, b, 8, 5, 10 is 6 and their variance…

The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8. If M is the mean deviation of the numbers about the mean, then 25 M is equal to :

Multiple Choice Options

  • A 60
  • B 55
  • C 50
  • D 45

Step-by-Step Verified Solution

∵\because x‾=6=a+b+8+5+105⇒a+b=7\overline x = 6 = {{a + b + 8 + 5 + 10} \over 5} \Rightarrow a + b = 7 ...... (i)

And σ2=a2+b2+82+52+1025−62=6.8{\sigma ^2} = {{{a^2} + {b^2} + {8^2} + {5^2} + {{10}^2}} \over 5} - {6^2} = 6.8

⇒a2+b2=25\Rightarrow {a^2} + {b^2} = 25 ..... (ii)

From (i) and (ii) (a, b) = (3, 4) or (4, 3)

Now mean deviation about mean

M=15(3+2+2+1+4)=125M = {1 \over 5}(3 + 2 + 2 + 1 + 4) = {{12} \over 5}

⇒25M=60\Rightarrow 25M = 60

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