1. **Stating the problem:** We are given two sets of data representing the number of points scored in games by two players, Sam and Dan. We need to find the mode and median for each player, compare their medians, analyze the skewness of their distributions, and compare their ranges. 2. **Mode:** The mode is the value that appears most frequently in a data set. 3. **Median:** The median is the middle value when the data is ordered from least to greatest. If there is an even number of data points, the median is the average of the two middle numbers. 4. **Range:** The range is the difference between the maximum and minimum values in the data set. 5. **Skewness:** Skewness describes the asymmetry of the data distribution. A distribution can be left-skewed (tail on the left), right-skewed (tail on the right), or symmetric. 6. **Data for Sam (top plot):** - Points: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 - Frequencies (from description): 7 dots above 14, 3 dots above 10 and 16, others not specified but implied fewer. 7. **Data for Dan (bottom plot):** - Points: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 - Frequencies: highest stack above 14 points, also dots at 10, 12, 14, 16. 8. **Finding the mode for Sam:** - Highest frequency is 7 dots at 14 points. - So, mode for Sam is $14$. 9. **Finding the mode for Dan:** - Highest frequency is also at 14 points. - So, mode for Dan is $14$. 10. **Finding the median for Sam:** - Total games = sum of frequencies (not fully given, but from the dots described: 7 + 3 + 3 + others). Assuming the data is symmetric around 14 with more dots at 14. - Since 14 has the highest frequency, median is likely $14$. 11. **Finding the median for Dan:** - Similarly, median is around $14$ as highest frequency is at 14. 12. **Comparing medians:** - Median for Sam = $14$ - Median for Dan = $14$ - So, medians are equal. 13. **Range for Sam:** - Minimum point = 2 - Maximum point = 24 - Range = $24 - 2 = 22$ 14. **Range for Dan:** - Minimum point = 10 (lowest dot mentioned) - Maximum point = 16 (highest dot mentioned) - Range = $16 - 10 = 6$ 15. **Comparing ranges:** - Range for Sam ($22$) is greater than range for Dan ($6$). 16. **Skewness:** - Sam's data has more dots at higher points (7 dots at 14), suggesting a right skew or symmetric. - Dan's data is concentrated between 10 and 16, suggesting less spread and possibly symmetric or slight skew. **Final answers:** - Mode for Sam: $14$ - Mode for Dan: $14$ - Median for Sam: $14$ - Median for Dan: $14$ - Range for Sam: $22$ - Range for Dan: $6$ - Sam's distribution has a wider range and possibly more skew than Dan's.