Question

1. which of the following boxplots best matches the distribution shown in the histogram? histogram with x - axis labeled data (0, 2, 4, 6, 8, 10, 12) showing two peaks (around 0 - 4 and 8 - 10) and a valley at 6; five boxplots (a) - (e) with x - axis 0 - 12 are shown below the histogram

Explanation:

Step1: Analyze the Histogram's Distribution

The histogram has two peaks (bimodal) around 0 - 2 and 10 - 12, with a valley in the middle (around 6 - 8). This means the data is bimodal, so the boxplot should reflect a distribution with two main clusters, likely having outliers or a spread that accounts for the two peaks.

Step2: Evaluate Each Boxplot

• Option (a): Symmetric boxplot, no indication of bimodality.
• Option (b): Has outliers (the dots) and the box is centered but with whiskers that could account for the two clusters. The bimodal distribution would likely have outliers or a spread that includes the two peaks, and the presence of outliers here matches the possibility of two separate clusters.
• Option (c): Skewed right, doesn't match bimodal.
• Option (d): Symmetric, narrow box, doesn't match bimodal.
• Option (e): Skewed right, doesn't match bimodal.

The bimodal histogram suggests the data has two groups, so the boxplot with outliers (option b) is the best match as it accounts for the two clusters (the outliers could be part of the two peaks or the spread includes both clusters).

Answer:

b. The boxplot with outliers (dots) at the ends, matching the bimodal histogram's two clusters.