Here is a step-by-step solution for determining which statement is most likely to be true based on the ages and standard deviations of the four swim teams:
1. Understand the concept:
Standard deviation is a measure of the amount of variation or dispersion in a set of values. A higher standard deviation indicates that the values are spread out over a wider range.
2. Given data:
- Stars: Mean = 16, Standard Deviation = 4.1
- Dolphins: Mean = 18, Standard Deviation = 1.5
- Giants: Mean = 14, Standard Deviation = 0.3
- Mackerels: Mean = 15, Standard Deviation = 2.3
3. Comparison of standard deviations:
To determine which team has the most dispersed ages from the mean, compare the standard deviation values for each team:
- Stars: Standard Deviation = 4.1
- Dolphins: Standard Deviation = 1.5
- Giants: Standard Deviation = 0.3
- Mackerels: Standard Deviation = 2.3
4. Identify the largest standard deviation:
The largest standard deviation among the given teams is 4.1.
5. Conclusion:
The team with the largest standard deviation is the Stars. Therefore, the statement most likely to be true is:
"The ages of the Stars are the most dispersed from the team's mean."
