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The mean and the standard deviation (sd) of five observations are 9 and 0, respectively. If one of the observations is changed, such that the mean of the new set of five observations becomes 10, then their sd is
  • a)
    0
  • b)
    2
  • c)
    4
  • d)
    1
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The mean and the standard deviation (sd) of five observations are 9 an...
Since the standard deviation before the change was 0, all the observations were exactly equal to 9.
Since one observation was changed and the new mean is 10, we have the following equation.
(9 + 9 + 9 + 9 + x)/5 = 10
(36 + x)/5 = 10
Solving for x, we have
x = 14
The changed observation is 14.
All the observations are {9, 9, 9, 9, 14}.
Since the mean is 10, the variance is
[(9 - 10)2 + (9 - 10)2 + (9 - 10)2 + (9 - 10)2 + (14 - 10)2]/5
= (1 + 1 + 1 + 1 + 16)/5
= 20/5
= 4
Hence, the standard deviation is √4 = 2
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The mean and the standard deviation (sd) of five observations are 9 and 0, respectively. If one of the observations is changed, such that the mean of the new set of five observations becomes 10, then their sd isa)0b)2c)4d)1Correct answer is option 'B'. Can you explain this answer?
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