Rationale
The range of the data set is 22.
To calculate the range of a data set, subtract the smallest value from the largest value. In this case, the smallest number is 8 and the largest is 30, so the range is 30 - 8 = 22.
A) A range of 9 would imply that the difference between the highest and lowest values is only 9. Given the largest value of 30 and the smallest value of 8, this is not accurate as their difference is much greater than 9.
B) A range of 14 would suggest that the highest and lowest values differ by only 14 units. However, with the smallest number being 8 and the largest number being 30, the actual difference is 22, making 14 an incorrect choice.
C) The range of 22 is correct because it accurately represents the difference between the highest value of 30 and the lowest value of 8 in the data set. Thus, the range is calculated as 30 - 8 = 22.
D) A range of 18 would indicate that the difference between the highest and lowest values is 18. However, this calculation does not hold true here, as the correct difference between 30 and 8 is 22, which makes 18 incorrect.
Conclusion
The range serves as a measure of the spread of a data set by determining the difference between the maximum and minimum values. In this example, the data set of 8, 22, 15, 30, 14, 26, and 17 yields a range of 22, affirming the significance of accurately identifying the highest and lowest values for such calculations.