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      Question

      The mean of 5 observations is 10 and their standard

      deviation is 4. Each observation is multiplied by 3 and then increased by 5. Find the new mean and the new standard deviation.
      A 33 and 10 Correct Answer Incorrect Answer
      B 35 and 12 Correct Answer Incorrect Answer
      C 21 and 18 Correct Answer Incorrect Answer
      D 18 and 5 Correct Answer Incorrect Answer

      Solution

      ATQ, If each observation is multiplied by a and then increased by b: New mean = a × (old mean) + b New standard deviation = |a| × (old SD) Here a = 3, b = 5. New mean = 3 × 10 + 5 = 35 New SD = 3 × 4 = 12

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