Final answer:
The assertion that whiskers extend to the smallest or largest observations within the fence in a box-and-whisker plot is false; they extend to the smallest and largest non-outlier observations.
Step-by-step explanation:
The statement that whiskers go to the smallest or largest observation within the fence is false. In a box-and-whisker plot, the whiskers extend from the first quartile to the smallest non-outlier value and from the third quartile to the largest non-outlier value. However, if outliers are present, these are marked with dots and the whiskers do not extend to them, but instead to the last data points that are not outliers.
It is relevant to note that the median is shown with a dashed line and is not involved in the whisker length determination. In cases where outliers are identified, the fence is utilized to determine what constitutes an outlier based on a calculated distance from the quartiles.