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
The mode is 91 along with the median (50th percentile), with all the scores lower. The mean acts as a fulcrum (balance point) for the distribution, which means it is most influenced by deviant scores.
This should lead you to the answer.
To determine which statement is true about the distribution of the scores, let's analyze the given information.
We are told that half of the students scored 91 on the achievement test. This indicates that the median score is 91, as half of the students scored below this value and half scored above it.
Next, we are informed that some students scored 47, while the remaining students scored 71. This suggests that 47 is the mode since it occurs more frequently compared to any other value.
Now, let's examine the given options:
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 the validity of each statement, we need to compare the values of the mean, median, and mode.
First, let's consider option a. Since we know that the median is 91 and some students scored 47, it is possible for the mean to be greater than the median. So option a could be true.
Next, let's evaluate option b. Given that the mode is 47, it is also plausible for the mean to be greater than the mode. Hence, option b could also be true.
Now, let's assess option c. Since the median is 91, it is not possible for the mean to be less than the median. Consequently, option c is not true.
Lastly, we examine option d. As we have seen, the mode is 47 and the mean can be greater than the mode. Therefore, option d is not true.
In conclusion, both options a and b could be true about the distribution of the scores.