Final answer:
A box plot provides a visual representation of the data's distribution, including the median, but does not show the mean. It is constructed using five values: the minimum, first quartile, median, third quartile, and maximum. A wider box plot indicates a greater spread in the middle 50 percent of the data.
Step-by-step explanation:
A box plot, or box-and-whisker plot, is a graphical representation of a data set that shows the distribution of the data. It is constructed from five main components: the minimum value, the first quartile (Q1), the median, the third quartile (Q3), and the maximum value. The box plot highlights the median of the data, but not the mean. To find the mean, one would need to perform a separate calculation, as the mean is the sum of all data values divided by the number of values, which cannot be determined solely by the box plot.
The box itself contains the middle 50 percent of the data, known as the interquartile range (IQR), and the whiskers extend to the smallest and largest values. If the first quartile is the same as the minimum value or the third quartile is the same as the maximum value, the whiskers might not be visible on one side of the box. The spread of the data within the box, between Q1 and Q3, shows the variability of the middle 50 percent of the data. A wider box indicates a greater spread in the data.