In a box and whisker plot, what is the primary function of the whiskers?

• A. They indicate the range of the data outside the interquartile range, typically extending to the smallest and largest values within $1.5\times \mathrm{IQR}$ from the quartiles.
• B. They show the frequency of each data value.
• C. They display the mode of the dataset.
• D. They represent the mean and standard deviation of the data.

Answer: (A)

Verified step by step guidance

1. Understand that a box and whisker plot is a graphical representation used to summarize the distribution of a dataset, highlighting key statistics such as the median, quartiles, and potential outliers.
2. Recognize that the 'box' in the plot represents the interquartile range (IQR), which is the range between the first quartile (Q1) and the third quartile (Q3). This captures the middle 50% of the data.
3. Identify that the 'whiskers' extend from the edges of the box (Q1 and Q3) to the smallest and largest data points that are within a certain distance from the quartiles, specifically within 1.5 times the IQR.
4. Note that any data points beyond the whiskers are considered outliers and are typically plotted individually to indicate values that fall outside the typical range of the data.
5. Conclude that the primary function of the whiskers is to indicate the range of the data outside the interquartile range but within 1.5 times the IQR, rather than showing frequency, mode, mean, or standard deviation.