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Question: Answered & Verified by Expert
The mean and standard deviation of 10 observations x1, x2, x3.....x10 are x¯ and σ respectively. Let 10 is added to x1, x2.....x9 and 90 is subtracted from x10. If still, the standard deviation is the same, then x10-x¯ is equal to
MathematicsStatisticsJEE Main
Options:
  • A 35
  • B 45
  • C 55
  • D 50
Solution:
2176 Upvotes Verified Answer
The correct answer is: 45
i=110xi-x¯210=σ21
i=19xi+10-x¯2+x10-90-x¯210=σ22
From 1 and (2)
i=110xi-x¯210=i=110xi-x¯2+20i=19xi-x¯-180x10-x¯+100×9+810010
2×i=19xi-x¯+2x10-x¯-20x10-x¯+90+810=0
900=20x10-x¯x10-x¯=45

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