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?

Rationale

The range does not change.

Adding a uniform bonus of $50 to each employee's earnings does not affect the difference between the highest and lowest earnings. Consequently, the range, defined as the difference between these two values, remains unchanged.

A (The range does not change) CORRECT

This statement is correct because the range is calculated by subtracting the minimum value from the maximum value. Since both the maximum and minimum values are increased by the same amount (the $50 bonus), their difference—and thus the range—remains the same.

B (The range increases by 50) YOUR ANSWER

This choice is incorrect because an increase in the range by $50 would imply that the difference between the highest and lowest earnings has changed. Since both values are increased uniformly, the range does not change at all.

C (The range increases by 100) YOUR ANSWER

This option is also incorrect for the same reason as choice B. A uniform increase to both the maximum and minimum earnings does not lead to a change in the range; it remains constant at $112, regardless of the bonuses.

D (The range increases by 500) YOUR ANSWER

This choice is incorrect as well. A change of $500 in the range would suggest a significant alteration in the spread of earnings, which is not possible when the same amount is added to each employee's earnings. The range remains at $112, unchanged by the bonuses.

Conclusion

When a uniform bonus is applied to all employees' earnings, the range remains unchanged, as both the maximum and minimum values are equally affected. Thus, the correct answer is that the range does not change, reinforcing the concept that adding a constant to all data points does not alter their relative differences.

The range does not change.

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