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

What is the variance (treating the data as a complete population) of the observations 2, 4, 6, 8 and 10?

The variance is 8. The mean is 6, the squared deviations sum to 40, and dividing by the 5 observations gives 8. Dividing by 4 would give 10, which is the sample variance, and 2.83 is the standard deviation, not the variance.

  1. A8Correct
  2. B10
  3. C40
  4. D2.83

Explanation

The mean is 30/5 = 6. The deviations are -4, -2, 0, 2 and 4, and their squares sum to 16+4+0+4+16 = 40. Population variance = 40/5 = 8. Dividing by n-1 gives 10, which is the sample variance and not what is asked. 40 is only the sum of squares, and 2.83 is the SD.

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