Final answer:
In a box and whisker plot, the box represents the middle 50 percent of the data, and the size of the box shows the spread of that data. The box's position and asymmetry can indicate a skewed distribution, as seen in datasets where the interquartile range is not symmetrical or when outliers are displayed.
Step-by-step explanation:
The box in a box and whisker plot shows where the middle 50 percent of the data is, indicating the interquartile range. The size of the box denotes the spread of the middle 50 percent of the data. However, the box does not always fall in the center of the data set. This can especially be observed in skewed distributions, where the median does not evenly divide the box, resulting in different lengths for each half of the box. For example, a dataset with exam scores where the lower spread is greater than the upper spread indicates a left-skewed distribution, with the left whisker longer than the right whisker. In such cases, the box plot may show a substantial number of higher scores while still displaying the variability in the lower scores.
One could think of a data set of age distribution for a specific product's buyers as an example. If the first and second quartiles are close together and the second to third quartiles are far apart, it suggests that there is less variability among the younger buyers, and more variability as age increases. This kind of distribution suggests a dataset that is skewed to the right. Besides, outliers may be presented with dots beyond the whiskers, emphasizing values that fall outside the typical range of the data.