The following are histograms of quiz scores for four different classes. Which distribution shows the MOST variability?

(Select the best answer)

Question

The following are histograms of quiz scores for four different classes. Which distribution shows the MOST variability?

(Select the best answer)

BlackTom AI · Accepted Answer

First, I will restate the question and the answer choices to be clear about what we are evaluating.
Question: The following are histograms (boxplots) of quiz scores for four different classes. Which distribution shows the MOST variability? (Select the best answer)
Answer options: Class 1, Class 2, Class 3, Class 4

Now, let's analyze each option in turn by considering variability, which is captured by the overall spread of the data (the distance from the smallest to largest values, i.e., the range, and the length of the box, i.e., the interquartile range).

- Class 1: On the blue boxplot, the whiskers extend from roughly 155 cm up to about 195 cm, and the box itself is fairly tall. This indicates a wide overall range and a relatively large IQR, suggesting high variability within this class.

- Class 2: The red boxplot shows a more compact spread. The whiskers are shorter than Class 1, and the box (IQR) is narrower as well, indicating less variability compared to Class 1.

- Class 3: The green boxplot has a moderate to wide range, with whiskers that extend quite a bit and a sizable box. However, when comparing to Class 1, the overall spread appears slightly less expansive, making variability substantial but not necessarily the largest.

- Class 4: If present in the chart, this distribution would be evaluated similarly by looking at its whisker length and box size. Compare its total spread to Class 1’s; if it’s smaller, then it shows less variability.

To identify the one with the MOST variability, we compare the total spread (range) and the IQR across all classes. The option with the widest overall spread and the tallest box generally signals the greatest variability.

Based on the visual assessment of the boxplots, Class 1 exhibits the widest reach from the lowest to highest values and a relatively large interquartile range, indicating the greatest variability among the four classes. In contrast, the other classes show noticeably tighter clustering (smaller ranges and/or smaller boxes).

Keep in mind that variability can be influenced by both the spread of the whiskers (range) and the height of the box (IQR); together these pieces show that Class 1 has the most spread.

COMM_V 191 201 202 203 204 2024W2 2024W2 COMM 191 Midterm - Friday, March 7, 2025

The following are histograms of quiz scores for four different classes. Which distribution shows the MOST variability? (Select the best answer)

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