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The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7, then the remaining two observations are:
  • a)
    10, 11
  • b)
    3, 18
  • c)
    8, 13
  • d)
    1, 20
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The mean of 6 distinct observations is 6.5 and their variance is 10.25...

x5 + x6 = 21
Let other two numbers be a, (21 - a)
Now,

(Using formula for variance)
⇒ 6(10.25) + 6(6.5)2 = 94 + a2 + (21 - a)2
⇒ a2 + (21 - a)2 = 221
∴ a = 10 and (21 - a) = 21 - 10 = 11
So, remaining two observations are 10, 11.
⇒ Option (a) is correct.
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The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7, then the remaining two observations are:a)10, 11b)3, 18c)8, 13d)1, 20Correct answer is option 'A'. Can you explain this answer?
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