The two sets of data below represent the number of runs scored by two different youth baseball teams over the course of a season. Team \( A: 4,8,5,12,3,9,5,2 \) Team \( B: 5,9,11,4,6,11,2,7 \) Which set of statements about the mean and standard deviation is true? A. mean \( A< \) mean \( B \) standard deviation \( A> \) standard deviation \( B \) B. mean \( A> \) mean \( B \) standard deviation \( A< \) standard deviation \( B \) C. mean \( A< \) mean \( B \) standard deviation \( A< \) standard deviation \( B \) D. mean \( A> \) mean \( B \) standard deviation \( A> \) standard deviation \( B \)

To find out which statements about the mean and standard deviation are true, let's calculate those metrics for each team. For Team A: Mean = (4 + 8 + 5 + 12 + 3 + 9 + 5 + 2) / 8 = 5.875 Standard Deviation = \( \sqrt{\frac{(4-5.875)^2 + (8-5.875)^2 + ... + (2-5.875)^2}{8}} \approx 2.95 \) For Team B: Mean = (5 + 9 + 11 + 4 + 6 + 11 + 2 + 7) / 8 = 6.875 Standard Deviation = \( \sqrt{\frac{(5-6.875)^2 + (9-6.875)^2 + ... + (7-6.875)^2}{8}} \approx 2.80 \) Now, we can compare the means and standard deviations: - Mean \( A < \) Mean \( B \) (5.875 < 6.875) - Standard Deviation \( A > \) Standard Deviation \( B \) (2.95 > 2.80) This means that option A is the correct answer: mean \( A < \) mean \( B \) and standard deviation \( A > \) standard deviation \( B \).