Final answer:
The statement about whiskers on a boxplot always extending to the minimum and maximum data values is False, as they extend to the nearest data points within 1.5 IQR of the quartiles unless there are outliers marked with dots.
Step-by-step explanation:
The statement "The whisker always extends to the minimum and maximum on a boxplot" is False. Whiskers on a box plot extend from the first quartile to the smallest data value within 1.5 IQR (interquartile range) below the first quartile, and from the third quartile to the largest data value within 1.5 IQR above the third quartile. Outliers that fall outside of these ranges are typically marked with dots, resulting in whiskers that do not reach the minimum or maximum data values if outliers exist.
When constructing a boxplot, the median, first quartile, and third quartile define the central box, representing approximately the middle 50% of the data. The position of the median within the box can give us a quick picture of the overall data distribution, indicating whether the data is skewed to the left, to the right, or is symmetric.