A box plot is constructed using which of the following pieces of data?

• A. The frequencies of each category
• B. The mean $\mu$ and standard deviation $\sigma$ only
• C. The mode and range only
• D. The minimum, first quartile $Q_1$, median $Q2$, third quartile $Q_3$, and maximum values

Answer: (D)

Verified step by step guidance

1. Understand that a box plot (or box-and-whisker plot) is a graphical representation used to display the distribution of a data set based on five summary statistics.
2. Identify the five-number summary that a box plot uses: the minimum value, first quartile (Q1), median (Q2), third quartile (Q3), and maximum value.
3. Recognize that these five values help visualize the spread and skewness of the data, showing the central tendency and variability without relying on mean or standard deviation.
4. Note that frequencies, mean, standard deviation, mode, and range are not directly used to construct a box plot, although they provide other useful information about the data.
5. Conclude that the correct data for constructing a box plot are the minimum, first quartile, median, third quartile, and maximum values.