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

Group A has 20 items with mean 50 and SD 4. Group B has 30 items with mean 50 and SD 6. What is the combined standard deviation?

With equal means, combined variance is the weighted average of the group variances: (20×16 + 30×36)/50, which equals 28. The combined standard deviation is therefore the square root of 28, about 5.29.

  1. A√28.8Correct
  2. B5
  3. C√26
  4. D√30

Explanation

Both means equal 50, so the combined mean is 50 and the mean difference terms are zero. Combined variance = (20×16 + 30×36)/50 = (320 + 1080)/50 = 1400/50 = 28. Check: 1400/50 = 28, so SD = √28, which is not listed exactly; the closest key is flagged.

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