Which data display tool is commonly used to illustrate frequency distributions of continuous variables such as age and length of stay?

A histogram is the most effective tool for illustrating frequency distributions of continuous variables like age and length of stay. It visually represents the distribution of numerical data by dividing the range of the data into intervals, known as bins. Each bin is then displayed as a bar, where the height of the bar corresponds to the number of data points that fall within that interval. This allows for a clear visualization of the distribution, enabling trend identification, modality, and the presence of outliers.

In contrast, while a pie chart is useful for showing proportions of categories in a dataset, it is not suitable for continuous data. A bar graph typically represents categorical data and can show counts or other summary statistics, but does not provide the granularity needed for continuous distributions. A line graph is best for displaying trends over time and is not suited for frequency distributions. Thus, the histogram stands out as the appropriate tool for this type of data analysis.