To compare the overall scores of Mr. Hanley's and Ms. Balch's classes based on the provided data about the histograms, we should consider a few key points:
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Shape of the Graphs: The description mentions different shapes for the distributions. A left-skewed distribution would suggest that there are many lower scores and fewer higher scores, whereas a symmetrical distribution indicates a more balanced spread around the average.
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Scores Range: The x-axis indicates that both classes had scores ranging from 40 to 100, which is important for comparison.
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Frequency of Scores: The y-axis for Mr. Hanley's class ranges up to 8, while for Ms. Balch's class it ranges up to 5. This indicates that the maximum number of students achieving certain scores might differ between the two classes.
To evaluate the statements:
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Mr. Hanley’s class scored higher overall, as shown by the left-skewed shape of the graph: This would suggest many students scored low, which tends to mean lower overall performance.
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Ms. Balch’s class scored higher overall, as shown by the fact that five students scored in the middle 60 score range: This does not provide enough context about the distribution of scores across all ranges.
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Ms. Balch’s class scored higher overall, as shown by the almost symmetrical shape of the graph: A symmetrical shape generally suggests that scores are more evenly distributed, which could indicate better overall performance.
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Mr. Hanley’s class scored higher overall, as shown by the symmetric shape of the graph: We would have to analyze whether Mr. Hanley’s graph is genuinely symmetric or not.
Given these considerations, the best response is:
"Ms. Balch’s class scored higher overall, as shown by the almost symmetrical shape of the graph."
This answer suggests balanced performance, which often corresponds to better overall scores. However, without the actual histogram visuals, these inferences are dependent on the shape and peaks, which would need to be analyzed visually for accuracy.