Without the visual histograms to analyze directly, we can infer the most likely conclusion based on common trends in shoe sizes concerning age groups. Younger boys (in 6th grade) typically have smaller feet compared to older boys (in 7th grade), so we likely see a trend where the average shoe size increases with age.
Here are the interpretations of each option based on this trend:
A. As boys get older, shoe sizes increase and the distribution remains relatively unchanged.
- This might be true if the relative shape of the distribution does not change much, but it doesn't address any potential outliers or variance.
B. As boys get older, shoe size range, defined by the minimum and maximum, decreases.
- This is unlikely, as older boys generally have larger feet which would likely increase the range.
C. As boys get older, shoe sizes become more normally distributed with fewer large outliers.
- This could be true if the size increases are more centered around a common average, but it contradicts the potential for larger outliers as boys grow.
D. As boys get older, shoe size distribution becomes more spread with more large outliers.
- This is likely true as older boys might have significantly larger shoe sizes, leading to a wider spread in the size distribution.
Based on these deductions, A and D could be plausible conclusions. However, given typical trends of growing shoe sizes with age and possibly more diverse ranges due to outliers in size, D is likely the best-supported conclusion.
Thus, the most supportable conclusion is D. As boys get older, shoe size distribution becomes more spread with more large outliers.
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