Scores from the same benchmark test are collected from two algebra classes, each with 30 students enrolled. One class had a mean score of 79 with a mean absolute deviation of 5, and on the other hand a mean score of 81 with the mean absolute deviation of 10. What can be said about the distribution of scores on this test for the two classes?
To understand the distribution of scores for the two classes, we can analyze the mean scores and the mean absolute deviations.
First, let's talk about the mean score. The mean score represents the average performance of the students in each class.
In the first class, the mean score is 79. This indicates that, on average, the students scored 79 on the test. In the second class, the mean score is 81, which means that, on average, the students scored 81 on the test.
Comparing these two mean scores, we can conclude that, on average, the students in the second class performed slightly better than those in the first class.
Now, let's move on to the mean absolute deviation (MAD). The MAD measures the average distance between each individual score and the mean score.
In the first class, the MAD is 5. This means that, on average, the individual scores in the first class are 5 units away from the mean score of 79. In the second class, the MAD is 10, indicating that the individual scores in the second class are, on average, 10 units away from the mean score of 81.
Comparing these two MAD values, we can conclude that the distribution of scores in the first class is more tightly clustered around the mean score of 79 (as the MAD is smaller), while the distribution in the second class is more spread out (as the MAD is larger).
In summary, based on the mean scores and mean absolute deviations, we can say that, on average, the students in the second class performed slightly better than those in the first class. However, the scores in the first class are more tightly clustered around the mean score, while the scores in the second class are more spread out.