Correct option is D
The correct answer is (d).
Introduction
Bowley's coefficient of skewness provides a method to measure the asymmetry of a dataset relying on quartiles and the median.
By applying the given values of the sum of quartiles, the median, and the skewness coefficient into the formula, we can establish a system of linear equations. Solving these equations reveals the precise values for the lower and upper quartiles.
- Bowley’s coefficient of skewness is defined as
- Here, is the lower quartile, is the upper quartile, and is the median.
- We are given
-
- This simplifies to
-
- Now, solving the system: and
- Adding the equations yields , and consequently
- Option A (40 and 60): If , their sum is 100, but . The skewness would be , which is incorrect.
- Option B (20 and 80): If , their sum is 100, but . The skewness would be , which is incorrect.
- Option C (30 and 60): The sum of these quartiles is 90, which violates the given condition that the sum of the quartiles must be exactly 100.