Based on the boxplots, which statement provides the best comparison of the two locations?

• A. $\mathrm{Location} B$ has a smaller interquartile range than $\mathrm{Location} A$, so its data are more spread out.
• B. Both locations have the same number of outliers, so their distributions must be identical.
• C. $\mathrm{Location} A$ has a higher median value than $\mathrm{Location} B$, indicating that its typical observation is greater.
• D. $\mathrm{Location} A$ and $\mathrm{Location} B$ have identical ranges and medians, so their distributions are the same.

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the components of a boxplot. A boxplot displays the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values of a dataset, as well as potential outliers.
2. Step 2: Identify the median values for both Location A and Location B from their boxplots. The median is the line inside the box and represents the middle value of the data.
3. Step 3: Compare the interquartile ranges (IQR) of the two locations. The IQR is calculated as \(\text{IQR} = Q3 - Q1\) and represents the spread of the middle 50% of the data.
4. Step 4: Examine the number of outliers in each location. Outliers are typically shown as individual points outside the whiskers of the boxplot and indicate extreme values.
5. Step 5: Use these observations to evaluate each statement: check if Location A has a higher median than Location B, if Location B has a smaller IQR, if the number of outliers is the same, and if the ranges and medians are identical. This will help determine which statement best describes the comparison.