Question

The company at which Mark is employed has 80 employees, each of whom has a different salary. Mark’s salary of 43,700 is the second-highest salary in the first quartile of the 80 salaries. If the company were to hire 8 new employees at salaries that are less than the lowest of the 80 salaries, what would Mark’s salary be with respect to the quartiles of the 88 salaries at the company, assuming no other changes in the salaries?

• A. The fourth-highest salary in the first quartile
• B. The highest salary in the first quartile
• C. The second-lowest salary in the second quartile
• D. The third-lowest salary in the second quartile
• E. The fifth-lowest salary in the second quartile

Hint:

When quartiles are recalculated after adding data, always recompute the group sizes and re-check the position of the given element.

Answer 1

The Correct Option is D

Step 1: Understanding quartiles.
For 80 employees, each quartile has \( \tfrac{80}{4} = 20 \) salaries. The first quartile consists of the lowest 20 salaries. Mark’s salary is the second-highest in this quartile, meaning it is the 19th salary overall.
Step 2: After hiring 8 new employees.
The company will then have 88 employees. Each quartile will now contain \( \tfrac{88}{4} = 22 \) salaries. The 22 lowest salaries will be in the first quartile, and the next 22 in the second quartile.
Step 3: Position of Mark’s salary.
Mark’s original position was 19th. With 8 new employees added at the bottom, his position becomes \( 19 + 8 = 27 \).
Step 4: Quartile placement.
- Quartile 1: positions 1–22
- Quartile 2: positions 23–44
Mark’s salary is now at position 27, which lies in Quartile 2.
Step 5: Relative position in Quartile 2.
In Quartile 2, Mark’s salary is \( 27 - 22 = 5 \)-th lowest. Thus, it is the third-lowest salary in the second quartile.
Step 6: Conclusion.
The correct answer is: \[ \boxed{\text{(D) The third-lowest salary in the second quartile.}} \]