103. If the range of the average annual earthquake frequencies in the table shown is 9.7, which of the following could be the value of x? (The range of a set of numbers is the difference between the greatest and the least numbers.)
Answer: D
The value of x could be 15.
The range of a set of numbers is calculated by subtracting the least number from the greatest number. Given that the range is 9.7, if x is the greatest number, then the least number must be x - 9.7. Therefore, x can be 15 when the least number is 5.3.
A) 1.3
If x is 1.3, the maximum value would be only 1.3. The least number would then be calculated as 1.3 - 9.7, resulting in a negative number (-8.4), which is not possible. Therefore, this option is incorrect.
B) 9.7
If x is 9.7, the least number would be 9.7 - 9.7, which equals 0. While this maintains a range of 9.7, it does not represent a scenario where there are greater values than the least number, making it less viable than option D. Thus, this option is not correct.
C) 12.7
If x is 12.7, the least value would be 12.7 - 9.7, resulting in 3.0. Although this configuration maintains the range of 9.7, it does not utilize the maximum potential for x, which can be higher. Therefore, this option is not the best answer.
D) 15
When x is 15, the least number would be calculated as 15 - 9.7, which equals 5.3. This scenario satisfies the condition of having a maximum value higher than the minimum while maintaining the correct range of 9.7. Thus, this option is correct.
Conclusion
The correct answer is D, as it provides a scenario where the maximum value (15) and the minimum value (5.3) maintain a range of 9.7, fulfilling the condition set by the question. Options A, B, and C either lead to invalid scenarios or do not fully utilize the range, making them incorrect.