Question

Mr. Hanley and Ms. Balch gave the same Algebra final exam to their classes. The histograms show the distribution of the scores for each class. Which best compares the overall scores of the two classes? (1 point) Responses Mr. Hanley’s class scored higher overall, as shown by the symmetric shape of the graph. Mr. Hanley’s class scored higher overall, as shown by the symmetric shape of the graph. Mr. Hanley’s class scored higher overall, as shown by the left-skewed shape of the graph. Mr. Hanley’s class scored higher overall, as shown by the left-skewed shape of the graph. Ms. Balch’s class scored higher overall, as shown by the fact that five students scored in the middle 60 score range. Ms. Balch’s class scored higher overall, as shown by the fact that five students scored in the middle 60 score range. Ms. Balch’s class scored higher overall, as shown by the almost symmetrical shape of the graph.

Answer 1

To determine which class scored higher overall based on the histogram shapes described, we need to analyze what the terms "symmetric shape," "left-skewed shape," and "almost symmetrical shape" imply about the distribution of scores.

• A symmetric shape usually indicates that the scores are evenly distributed around the mean, suggesting that most students scored around the average.
• A left-skewed shape indicates that the majority of scores were higher, with a tail extending towards the lower scores, which implies that some students scored poorly but a significant number scored well.
• An almost symmetrical shape suggests a more balanced distribution, but may not be perfectly centered, potentially indicating that some students scored higher, softening the extremes.

Given these definitions, if Mr. Hanley’s class has a left-skewed shape, it suggests that his students generally scored above average, while Ms. Balch's class with an almost symmetrical shape indicates a more balanced distribution of scores.

From the options provided:

1. Mr. Hanley’s class scored higher overall, as shown by the symmetric shape of the graph. (Inconsistent if the graph is left-skewed)
2. Mr. Hanley’s class scored higher overall, as shown by the left-skewed shape of the graph. (This is plausible if his class indeed shows higher scores in the majority)
3. Ms. Balch’s class scored higher overall, as shown by the fact that five students scored in the middle 60 score range. (This alone doesn't indicate higher overall performance)
4. Ms. Balch’s class scored higher overall, as shown by the almost symmetrical shape of the graph. (This could likely imply a reasonably average performance)

To conclude, the best comparison would depend on the actual details of the histograms, but if Mr. Hanley’s class indeed shows a left-skewed distribution, option 2 ("Mr. Hanley’s class scored higher overall, as shown by the left-skewed shape of the graph.") would be the most appropriate response, as it indicates that more students scored higher overall compared to Ms. Balch's class.