CA Foundation · Quantitative Aptitude · Measures of Central Tendency and Dispersion
For a distribution, the quartile deviation is 10 and the coefficient of quartile deviation is 0.25. What is the value of the third quartile?
The third quartile is 50. The quartile deviation of 10 gives Q3 − Q1 = 20, and the coefficient of 0.25 gives Q3 + Q1 = 80. Solving the two equations gives Q3 = 50 and Q1 = 30.
- A50Correct
- B30
- C40
- D60
Explanation
QD = (Q3 − Q1)/2 = 10, so Q3 − Q1 = 20. Coefficient = (Q3 − Q1)/(Q3 + Q1) = 20/(Q3 + Q1) = 0.25, so Q3 + Q1 = 80. Adding the two equations gives 2Q3 = 100, so Q3 = 50 and Q1 = 30. The value 30 is Q1, and 40 is the average of the quartiles.
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