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COMEDK20269 May 2026Evening ShiftMathematicsStatisticsActual

The variance of a set of 20 observations is 16. If 7 is added to each observation, and then 5 is subtracted from each resulting observation, what will be the new standard deviation ?

Options

  1. A2
  2. B9
  3. C18
  4. D4

Correct answer

D. 4

Step-by-step solution

The original variance of the observations is 16 . The original standard deviation is 16 = 4 . When 7 is added and then 5 is subtracted from each observation, the net effect is that 2 is added to each observation. The standard deviation of a dataset is independent of the change of origin. This means adding or subtracting a constant from each observation does not change the standard deviation. Therefore, the new standard deviation remains 4 . Answer: 4

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