To determine which class scored higher overall based on the information provided about the histograms, we need to consider the implications of the shapes of the distributions.
-
Left-skewed shape: This indicates that there are some lower scores bringing down the average, but most of the scores are higher. This suggests that Mr. Hanley’s class might have a few low performers, but overall, the majority scored fairly well.
-
Symmetric shape: A symmetric distribution generally indicates that scores are evenly spread around the average, suggesting that there is a balance in performance. If Mr. Hanley’s class had a symmetric distribution, that typically suggests an average score would be more moderate and not overly skewed towards high or low.
-
Almost symmetrical shape: This could indicate consistency in scores and a good overall performance with no significant outliers.
Given these interpretations, we can analyze the statements in the question:
- If Ms. Balch's class had five students in a middle range but Mr. Hanley’s class was left-skewed, that suggests lower overall scores for Mr. Hanley's class, and therefore Ms. Balch's class would likely score higher.
An overall assessment would ideally need numerical data points or actual visual representations from the histograms; however, using reasoning based on the descriptions offered in the responses, "Ms. Balch’s class scored higher overall, as shown by the fact that five students scored in the middle 60 score range" would be a viable conclusion if the middle score range indicated a higher overall average score compared to Mr. Hanley’s left-skewed results.
So, the best interpretation would conclude with the first response:
Ms. Balch’s class scored higher overall, as shown by the fact that five students scored in the middle 60 score range.