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ACCA Applied Knowledge · Management Accounting · Summarising and analysing data

A company records the number of units produced per shift over ten shifts. Output was 10 units in 2 shifts, 20 units in 6 shifts and 30 units in 2 shifts. Treating the ten shifts as the whole population, what is the variance of output per shift?

The variance is 40. The mean output is 20 units, and the frequency-weighted sum of squared deviations is 400. Dividing by the ten shifts gives 40. The figure 6.32 would be the standard deviation, which is the square root of the variance.

  1. A40Correct
  2. B6.32
  3. C44.4
  4. D400

Explanation

The mean is (2x10 + 6x20 + 2x30)/10 = 200/10 = 20. The sum of f(x - mean)^2 = 2x100 + 6x0 + 2x100 = 400. The variance is 400/10 = 40. 6.32 is the standard deviation. 44.4 divides by 9 (the sample formula). 400 is the sum of squares before dividing by the frequency.

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