14. The following list shows the regular daily earnings of the 10 employees who work in an office: $176, $176, $200, $200, $200, $152, $128, $184, $240, $240. On a certain day, each of the 10 employees is given a bonus of $50 in addition to that employee's regular earnings. Which of the following statements best describes the change to the range of the regular daily earnings of the 10 employees when the bonuses are added?
Answer: A
The range does not change
When each employee receives a $50 bonus, the range of their regular daily earnings remains unchanged because the adjustment is uniform across all employees. The range is determined by the difference between the highest and lowest earnings, which will remain the same after the bonuses are added.
A) The range does not change
This option is correct because applying the same amount of bonus to each employee does not affect the relative difference between the highest and lowest regular earnings. The highest regular earning is $240, and the lowest is $128, so the range remains $240 - $128 = $112, regardless of the bonuses.
B) The range increases by 50
This option is incorrect because the range is not affected by adding a constant value to all data points. Since the same amount is added to each employee's earnings, the highest and lowest values are still the same in relation to each other.
C) The range increases by 100
This option is incorrect for the same reason as option B. Adding a uniform bonus does not change the difference between the maximum and minimum values. Therefore, the range does not increase at all.
D) The range increases by 500
This option is also incorrect, as it suggests a significant change that does not occur when a constant is added to all values. The range remains the same, and a change of 500 is impossible under these circumstances.
Conclusion
The correct answer is A, as adding a uniform bonus to all employees does not alter the range of their regular daily earnings. Options B, C, and D incorrectly suggest changes to the range that are not applicable in this scenario, reinforcing that the uniform adjustment keeps the range constant.