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 7. which of the following statements is true about the distribution of 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

Since half the class scored 91, the median should be around 91. When you average the low scores, especially the 7, it should bring the mean down to be lower than the median.

11, 4, 6, 7, 5, 10, 9, 21, 3, 0

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

First, we know that half of the students scored 91. This indicates that half of the scores are clustered around 91.

Next, we are told that with the exception of a few students who scored 47, the remaining students scored 7. This suggests that there are a few outliers at 47, but most of the other scores are closer to 7.

Now, let's consider each statement and determine if it is true or false based on the given information:

A: The mean is greater than the median.
- To determine this, we need to compare the average (mean) of the scores to the middle value (median) of the scores. Since half of the students scored 91, and the other half is split between 47 and 7, we can infer that the median will be closer to 91. Since 91 is greater than 7 (the majority of the scores), it is likely that the mean is also greater than the median. Thus, statement A is true.

B: The mean is greater than the mode.
- The mode represents the score(s) that occur most frequently. From the information given, it is clear that the mode is 91 since half of the students scored this value. As we have already determined that the majority of the scores are closer to 7, the mean is likely to be greater than the mode. Hence, statement B is true.

C: The mean is less than the median.
- As previously explained, the median is likely to be closer to 91, while the majority of the scores are closer to 7. Since 91 is greater than 7, the mean is unlikely to be less than the median. Therefore, statement C is false.

D: The mean and the mode are the same.
- We have already determined that the mode is 91, representing the most frequently occurring score. However, since the majority of the scores are closer to 7, it is highly unlikely that the mean and the mode will be the same. Consequently, statement D is false.

In conclusion, the correct statements about the distribution of scores are:
A: The mean is greater than the median.
B: The mean is greater than the mode.