in a mathematics class, half of the students scored 91 on an achievement test. with the exception of a few students who scored 47, the remaining students scored 71. which of the following statements is true about the distribution of the scores?

a: the mean is greater than the median
b: the mean is greater than the mode
c: the mean is less than the median
d: the mean and the mode are the same

To determine which statement is true about the distribution of scores, let's analyze the given information step by step.

1. Half of the students scored 91 on the achievement test: This means that 50% of the students received a score of 91.

2. Except for a few students who scored 47, the remaining students scored 71: This implies that the other 50% of the students obtained a score of 71, except for a few students who scored 47.

Now, let's consider each statement and evaluate its validity:

a) The mean is greater than the median: To calculate the mean, we need to find the average of all the scores. The median is the middle value when the scores are arranged in ascending or descending order.

Since half of the students scored 91 (which is higher than 71), the mean would be greater than the median. Therefore, statement a) is true.

b) The mean is greater than the mode: The mode refers to the value(s) that appear the most frequently. In this scenario, the mode would be 71, as it is the most common score among the students.

Since the mean is the average of all scores, which includes both 91 and 71, it would be greater than the mode. Hence, statement b) is true.

c) The mean is less than the median: Based on our previous analysis, we concluded that the mean is greater than the median. Therefore, statement c) is false.

d) The mean and the mode are the same: As mentioned earlier, the mode is equal to 71, while the mean is a combination of both 91 and 71. Thus, the mean and the mode in this case are different. Consequently, statement d) is false.

Therefore, the correct statements about the distribution of the scores are a) The mean is greater than the median and b) The mean is greater than the mode.