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ACCA Applied Knowledge · Management Accounting · Summarising and analysing data

A set of monthly cost observations has a mean of $50 and a standard deviation of $8. Each observation is multiplied by 2 and then $10 is subtracted from the result. What are the mean and standard deviation of the new data?

The new mean is $90 and the new standard deviation is $16. Multiplying by 2 and subtracting 10 changes the mean to 50 x 2 - 10 = 90. Subtracting a constant does not change spread, so the standard deviation is just 8 x 2 = 16.

  1. AMean $90, standard deviation $16Correct
  2. BMean $90, standard deviation $6
  3. CMean $90, standard deviation $32
  4. DMean $100, standard deviation $16

Explanation

The mean is transformed in the same way as each observation: 50 x 2 - 10 = 90. The standard deviation is affected only by the multiplier, not by a constant subtracted: 8 x 2 = 16. Subtracting 10 from the standard deviation gives 6, which is wrong. A standard deviation of 32 comes from scaling the variance (64 x 4 = 256) and wrongly treating it as the standard deviation. A mean of 100 ignores the subtraction.

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