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CA Foundation · Quantitative Aptitude · Measures of Central Tendency and Dispersion

For a variable x, the mean is 50 and the standard deviation is 8. A new variable y is defined as y = 5 − 3x. What is the variance of y?

The variance of y is 576. Adding the constant 5 does not change spread, and multiplying by −3 scales the standard deviation to 3×8 = 24, so variance is 24² = 576. The sign is irrelevant, and the variance scales by 9.

  1. A64
  2. B192
  3. C24
  4. D576Correct

Explanation

Variance is unaffected by change of origin (the constant 5) but is multiplied by the square of the scale factor. Since the factor is −3, the SD of y = 3 × 8 = 24 and the variance = 24² = 576. The value 24 is the SD, and 192 comes from multiplying the variance by 3 instead of 9.

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