Final answer:
The question involves mathematical concepts like mean, median, mode, and the impact of outliers on these measures. The mean age is 7.7, the median is 7.5, and the mode is 7, indicating a likely right-skewed age distribution. Not all provided statements are correct; they must be verified against the data specifics.
Step-by-step explanation:
The question about the ages of 10 boys on a soccer team requires analyzing measures of center (mean, median, mode) and understanding the effects of outliers on these measures. When examining the given information, it is revealed that the mean age is 7.7 years, the median age is 7.5 years, and the mode is 7 years. This implies that most boys on the team are 7 years old, the center of the age data is about 7.5 to 7.7 years old, and the distribution of ages is possibly right-skewed since the mean is higher than the median.
Regarding the initial statements:
- All players' ages fall within 2 years of each other, which might be checked against the provided data.
- The difference between the mean and median is not exactly 2, so statement 2 is incorrect.
- The mean and median are close, indicating they both represent the center of the data set well, as supported by statement 3.
- Presence of an outlier (age 8) suggests the mean may not be the best measure of center, supporting statement 4.
- The statement that the most common age is 7 correlates with the mode, confirming statement 5 is correct.
Each conclusion about the dataset must be directly checked against the provided data, which is essential before confirming the accuracy of the statements.