if this are class scores and in one week i have bimodal distribution,another week a positive skew,3rd week a normal distribution and 4th week negative skew.what does this different scores tells you about thios tests , what is happening to the students scores overtime. what type of distribution would the instructor most want to see if the best result is that most students earn an average score

The different types of distributions you mentioned (bimodal, positive skew, normal, and negative skew) give us insights into the distribution of the students' scores over time.

1. Bimodal distribution: This means that there are two distinct peaks in the scores, indicating that two groups of students performed significantly differently. It suggests that the class is divided into two subgroups: one group that performed well and another group that performed poorly.

2. Positive skew: A positively skewed distribution means that most of the scores are concentrated towards the lower end, with a few high outliers. In this case, the majority of students scored lower, while a few students achieved exceptionally high scores.

3. Normal distribution: This is the ideal distribution for most situations. A normal distribution means that the majority of students achieved average scores, with an equal number of students below and above the average.

4. Negative skew: On the contrary to positive skew, a negatively skewed distribution indicates that most of the scores are concentrated towards the higher end, with a few low outliers. Here, a majority of students scored higher, while only a few students received very low scores.

Considering the goal of most students earning an average score, the instructor would likely prefer a normal distribution. This means that the majority of students scored around the average, without any significant skewness or bimodal patterns that would indicate a significant division between high and low performers. A normal distribution shows that the majority of students are performing at an expected level, which aligns with the idea of an average score.