To determine which set has the greatest range, we need to calculate the range for each set individually. The range of a set is found by subtracting the smallest number in the set from the largest number in the set.
1. First Set: [tex]\(\{10, 14, 8, 19, 22, 13, 44\}\)[/tex]
- Minimum: [tex]\(8\)[/tex]
- Maximum: [tex]\(44\)[/tex]
- Range: [tex]\(44 - 8 = 36\)[/tex]
2. Second Set: [tex]\(\{19, 16, 50, 18, 29, 23, 37\}\)[/tex]
- Minimum: [tex]\(16\)[/tex]
- Maximum: [tex]\(50\)[/tex]
- Range: [tex]\(50 - 16 = 34\)[/tex]
3. Third Set: [tex]\(\{11, 9, 31, 29, 15, 17, 20, 24\}\)[/tex]
- Minimum: [tex]\(9\)[/tex]
- Maximum: [tex]\(31\)[/tex]
- Range: [tex]\(31 - 9 = 22\)[/tex]
4. Fourth Set: [tex]\(\{12, 6, 24, 20, 44, 15, 29\}\)[/tex]
- Minimum: [tex]\(6\)[/tex]
- Maximum: [tex]\(44\)[/tex]
- Range: [tex]\(44 - 6 = 38\)[/tex]
Now let's compare the ranges:
- First Set: [tex]\(36\)[/tex]
- Second Set: [tex]\(34\)[/tex]
- Third Set: [tex]\(22\)[/tex]
- Fourth Set: [tex]\(38\)[/tex]
The set with the greatest range is the fourth set, [tex]\(\{12, 6, 24, 20, 44, 15, 29\}\)[/tex], which has a range of [tex]\(38\)[/tex].
