1. **State the problem:** We are comparing two box plots representing heights of hockey and volleyball players. We need to determine which statements about variability, height differences, interquartile ranges, and medians are valid. 2. **Analyze statement A:** "There is more variability in the heights of the hockey players than the volleyball players." - Variability can be estimated by the range (max - min). - Hockey players' range: $84 - 64 = 20$ inches. - Volleyball players' range: $88 - 60 = 28$ inches. - Since $28 > 20$, volleyball players have more variability. - **Statement A is false.** 3. **Analyze statement B:** "The difference in height between the tallest players on both teams is 6 inches." - Tallest hockey player: 84 inches. - Tallest volleyball player: 88 inches. - Difference: $88 - 84 = 4$ inches. - **Statement B is false.** 4. **Analyze statement C:** "The interquartile range (IQR) in the data sets is the same." - IQR is the length of the box (Q3 - Q1). - Hockey players' box: approximately from 66 to 80 inches. - IQR hockey: $80 - 66 = 14$ inches. - Volleyball players' box: approximately from 68 to 76 inches. - IQR volleyball: $76 - 68 = 8$ inches. - Since $14 \neq 8$, IQRs are not the same. - **Statement C is false.** 5. **Analyze statement D:** "The median height of the volleyball players is 4 inches taller than the hockey players." - Median hockey: about 72 inches. - Median volleyball: about 76 inches. - Difference: $76 - 72 = 4$ inches. - **Statement D is true.** **Final answer:** Only statement D is valid.