Final answer:
After multiplying each number in the data set by 17 and ordering the results, the median of the new data set is the middle value, which is 476.
Step-by-step explanation:
If each of the numbers in the data set 28, 58, 20, 14, 18, 71, 36 were multiplied by 17, to find the median, we would have to first multiply each number by 17 and then order the resulting numbers. After sorting these numbers, the middle number would represent the median of the new data set.
Firstly, multiply each number in the set by 17:
- 28 × 17 = 476
- 58 × 17 = 986
- 20 × 17 = 340
- 14 × 17 = 238
- 18 × 17 = 306
- 71 × 17 = 1207
- 36 × 17 = 612
Next, order the resulting numbers from smallest to largest: 238, 306, 340, 476, 612, 986, 1207. The middle number, which is the fourth number when ordered, is 476. So the median of the new data set is 476.
Hence, the correct answer is (C) 476.