Question

Final exam scores for the students from two different classrooms are shown below. Class A: 50, 52, 53, 54, 55, 59, 60, 64, 67, 69, 80, 80, 80, 80, 83, 85, 90, 92, 92, 96 Class B: 51, 57, 61, 61, 67, 69, 69, 69, 70, 70, 79, 83, 84, 85, 86, 88, 93, 94, 97, 99 Which statement regarding the two data sets is true? A. The median of Class A is smaller than the median of Class B, whereas the means are the same for both classes. B. The mean of Class A is smaller than the mean of Class B, whereas the medians are the same for both classes. C. The mean of Class B is smaller than the mean of Class A, whereas the medians are the same for both classes. D. The median of Class B is smaller than the median of Class A, whereas the means are the same for both classes.

Answer 1

By calculating the mean and median for both Class A and Class B, we find that the median of Class A is smaller than Class B and the mean of Class A is also smaller than Class B. The correct statement regarding the two data sets is option B.

Step-by-step explanation:

When comparing the final exam scores for Class A and Class B, we must calculate the mean and median for each class in order to determine the correct statement. The mean is calculated by adding all the scores together and dividing by the number of scores, and the median is the middle value when the scores are arranged in ascending order.

For Class A, we arrange the scores in ascending order and find the median to be the average of the 10th and 11th values, since there are an even number of scores, which results in the median of (69+80)/2 = 74.5. The total of all scores is 1421 and dividing this by 20 (number of students), gives us a mean of 71.05.

For Class B, similarly, we find the median to be the average of the 10th and 11th values, which results in the median of (70+70)/2 = 70. The total of all scores is 1517 and dividing this by 20 gives us a mean of 75.85.

Comparing the results, we see that Class A has a smaller median than Class B, whereas the mean of Class A is also smaller than the mean of Class B. Therefore, based on our calculations, option B is the correct statement.