Consider the distribution of mathematics SAT scores of students in honors calculus at a liberal arts college. What would you expect the shape and variation of the distribution to be?
A. Symmetric with little variation
B. Symmetric with large variation
C. Skewed right with large variation
D. Skewed left with little variation
Answer B
Since you are dealing with a select group, I would expect little variation.
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To determine the shape and variation of the distribution of mathematics SAT scores for students in honors calculus at a liberal arts college, we can consider the characteristics of the data and draw conclusions based on that information.
In this scenario, the data represents mathematics SAT scores, which are typically continuous numerical values. The distribution of these scores would be expected to show some variation since different students will have different levels of performance on the test.
When it comes to the shape of the distribution, a symmetric distribution means that the data is evenly distributed around the central point. In this case, it would mean that an equal number of students scored below and above the mean score. A skewed distribution, on the other hand, indicates that the data is not evenly distributed around the central point, with more scores either on one side (skewed left) or the other (skewed right) of the mean.
Given that the distribution represents the performance of students in honors calculus at a liberal arts college, it is reasonable to expect that the students in this group are academically driven and have relatively high mathematics SAT scores. Therefore, we would not expect a skewed distribution with most scores located on one side.
However, since the student group in question is honors calculus, it is likely that there will still be a variation in the scores, as students at this level may have different levels of proficiency and preparation.
Based on these considerations, the most appropriate answer would be B. Symmetric with large variation. This implies that the distribution of mathematics SAT scores among students in honors calculus at the liberal arts college would be symmetric around the mean score, but with considerable variation among the scores.