A box-and-whisker plot is shown for a dataset. Which of the following statements about the box-and-whisker plot is not true?

• A. The box in a box-and-whisker plot represents the $\mathrm{interquartile} \mathrm{range}$, which contains the middle $50\%$ of the data.
• B. A box-and-whisker plot is an appropriate tool for visualizing $\mathrm{qualitative} \left(\mathrm{categorical}\right)$ data.
• C. The whiskers in a box-and-whisker plot usually extend to the $\mathrm{minimum}$ and $\mathrm{maximum}$ values that are not outliers.
• D. A box-and-whisker plot is typically used to display the distribution of $\mathrm{quantitative}$ data.

Answer: (B)

Verified step by step guidance

1. Step 1: Understand what a box-and-whisker plot represents. It is a graphical summary of a dataset that shows the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values, often highlighting the interquartile range (IQR) which contains the middle 50% of the data.
2. Step 2: Recognize that the box in the plot represents the interquartile range (IQR), which is the range between Q1 and Q3, containing the central 50% of the data points.
3. Step 3: Know that the whiskers typically extend from the box to the smallest and largest data points that are not considered outliers, thus showing the spread of the majority of the data.
4. Step 4: Recall that box-and-whisker plots are designed for quantitative (numerical) data because they rely on ordering and measuring distances between data points, which is not possible with qualitative (categorical) data.
5. Step 5: Identify the false statement by comparing each option to these facts. The incorrect statement is the one claiming that a box-and-whisker plot is appropriate for visualizing qualitative data, since it is actually used for quantitative data.