To determine which data set has the greatest spread, we need to calculate the range for each data set. The range is defined as the difference between the maximum and minimum values within a set.
Step-by-step solution:
### Set \(A\)
- Elements: \(84, 91, 87, 77, 94, 89, 74\)
- Minimum value: \(74\)
- Maximum value: \(94\)
- Range: \(94 - 74 = 20\)
### Set \(B\)
- Elements: \(89, 73, 84, 91, 87, 77, 94\)
- Minimum value: \(73\)
- Maximum value: \(94\)
- Range: \(94 - 73 = 21\)
### Set \(C\)
- Elements: \(73, 84, 89, 88, 77, 91, 87, 90\)
- Minimum value: \(73\)
- Maximum value: \(91\)
- Range: \(91 - 73 = 18\)
### Set \(D\)
- Elements: \(84, 89, 88, 82, 91, 87, 99\)
- Minimum value: \(82\)
- Maximum value: \(99\)
- Range: \(99 - 82 = 17\)
Summarizing the ranges:
- Set \(A\): \(20\)
- Set \(B\): \(21\)
- Set \(C\): \(18\)
- Set \(D\): \(17\)
The data set with the greatest spread is Set \(B\) with a range of 21.
Thus, the correct answer is:
B. Set [tex]\(B\)[/tex]
