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

Eight sorted observations are 10, 12, 15, 18, 22, 25, 30 and 34. Using Q1 = size of the (n+1)/4th item and Q3 = size of the 3(n+1)/4th item, with interpolation, what is the quartile deviation?

The quartile deviation is 8. Interpolation gives Q1 = 12.75 and Q3 = 28.75. Half of their difference, (28.75 − 12.75)/2, is 8. The figure 16 is the interquartile range, not the quartile deviation.

  1. A8Correct
  2. B16
  3. C20.75
  4. D6.5

Explanation

(n+1)/4 = 2.25, so Q1 = 12 + 0.25×3 = 12.75. 3(n+1)/4 = 6.75, so Q3 = 25 + 0.75×5 = 28.75. QD = (28.75 − 12.75)/2 = 8. The value 16 is the interquartile range, and 6.5 comes from wrongly taking the 2nd and 6th items without interpolation.

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