Define the five-number summary, and explain how to depict it visually with a boxplot. Which five numbers are included in the five-number summary for a data set? A. low value, variance, mean, standard deviation, and high value B. low value, lower quartile, mean, upper quartile, and high value C. Iow value, variance, median, standard deviation, and high value D. Iow value, lower quartile, median, upper quartile, and high value

The five-number summary consists of the following values: 1. **Minimum (low value)**: The smallest observation in the data set. 2. **Lower Quartile (first quartile, \(Q_1\))**: The median of the lower half of the data (not including the overall median if the number of observations is odd). 3. **Median**: The middle value of the data set. 4. **Upper Quartile (third quartile, \(Q_3\))**: The median of the upper half of the data. 5. **Maximum (high value)**: The largest observation in the data set. A boxplot is a graphical representation of this five-number summary. Here's how to depict it visually: - **Box:** The box is drawn from \(Q_1\) to \(Q_3\). A line is drawn inside the box at the median. - **Whiskers:** Lines (whiskers) extend from the box out to the minimum and maximum values. Thus, the five numbers included in the five-number summary are: low value, lower quartile, median, upper quartile, and high value. The correct answer is: **D. low value, lower quartile, median, upper quartile, and high value**.