A group of middle school boys have a mean height of 167 cm and vary from 164 cm to 169 cm. A group of high school boys have a mean height of 180 cm and vary from 175 cm to 183 cm. Which statement BEST compares the two groups of boys?
Responses
A Half of the high school boys are between 181 cm and 183 cm in height.Half of the high school boys are between 181 cm and 183 cm in height.
B On average, the middle school boys are taller. On average, the middle school boys are taller.
C The middle school boys vary in height more than the high school boys.The middle school boys vary in height more than the high school boys.
D For these groups, every high school boy is taller than every middle school boy.For these groups, every high school boy is taller than every middle school boy.
the correct answer is D, for these groups every high school boy is taller than every middle school boy.
Thank you for correcting me. As an AI language model, I strive to improve my responses and learn from my mistakes. You are correct, the best statement that compares the two groups of boys is D: "For these groups, every high school boy is taller than every middle school boy." This comparison highlights the difference in height between the two groups and shows that the high school boys are uniformly taller than the middle school boys.
To compare the two groups of boys, we need to consider their mean height and the range of heights within each group.
The mean height represents the average height of the boys in each group. In this case, the mean height of the middle school boys is 167 cm, while the mean height of the high school boys is 180 cm.
The range of heights gives us information about how much the heights vary within each group. The middle school boys have a range of heights from 164 cm to 169 cm, which means the difference between the tallest and shortest boy in the group is 5 cm. On the other hand, the high school boys have a range of heights from 175 cm to 183 cm, which means the difference between the tallest and shortest boy in the group is 8 cm.
Now, based on this information:
- Statement A: This statement does not provide any information about the mean height or the range of heights, so it cannot be used to compare the two groups.
- Statement B: This statement suggests that, on average, the middle school boys are taller. However, since the mean height of the high school boys is 180 cm, which is higher than the mean height of the middle school boys (167 cm), this statement is not correct.
- Statement C: This statement suggests that the middle school boys vary in height more than the high school boys. Since the range of heights for the middle school boys (5 cm) is smaller than the range of heights for the high school boys (8 cm), this statement is not correct.
- Statement D: This statement suggests that every high school boy is taller than every middle school boy. Since we only have information about the mean height and the range of heights, we cannot make this assertion. Therefore, this statement is not correct.
Based on the given information, the best statement to compare the two groups of boys is: "On average, the high school boys are taller." This statement reflects the higher mean height of the high school boys (180 cm) compared to the middle school boys (167 cm).