To determine which distribution of data has the largest standard deviation, we should compare the standard deviations of each distribution.
Here are the distributions and their respective standard deviations:
1. Distribution: [tex]\(1, 1, 1, 1, 4, 4, 7, 7, 7, 7\)[/tex]
- Standard Deviation: Approximately 2.683
2. Distribution: [tex]\(1, 1, 1, 4, 4, 4, 4, 7, 7, 7\)[/tex]
- Standard Deviation: Approximately 2.324
3. Distribution: [tex]\(1, 1, 4, 4, 4, 4, 4, 4, 7, 7\)[/tex]
- Standard Deviation: Approximately 1.897
4. Distribution: [tex]\(1, 4, 4, 4, 4, 4, 4, 4, 4, 7\)[/tex]
- Standard Deviation: Approximately 1.342
Comparing these standard deviations:
- The first distribution has a standard deviation of 2.683.
- The second distribution has a standard deviation of 2.324.
- The third distribution has a standard deviation of 1.897.
- The fourth distribution has a standard deviation of 1.342.
The largest standard deviation is 2.683, which corresponds to the first distribution: [tex]\(1, 1, 1, 1, 4, 4, 7, 7, 7, 7\)[/tex].
Thus, the distribution [tex]\(1, 1, 1, 1, 4, 4, 7, 7, 7, 7\)[/tex] has the largest standard deviation.
