Which tool is primarily used to illustrate a distribution of values ordered by frequency?

The appropriate tool to illustrate a distribution of values ordered by frequency is the histogram. A histogram displays the frequency of data points within specified intervals or ranges, allowing for a clear visual representation of how the values are distributed across these intervals. Each bar in a histogram corresponds to a range of values (called bins), and the height of the bar indicates the number of observations within that range. This makes it particularly useful for understanding the underlying distribution of the data.

The other options serve different purposes; for instance, a line graph is primarily used to depict trends over time, connecting data points with a line to show increases or decreases. A Pareto diagram is a specialized type of bar chart that focuses on identifying the most significant factors in a dataset based on frequency, but it does not display the distribution in the same way a histogram does. A bar chart, while visually similar to a histogram, is generally used to compare different categories rather than to show the distribution of a continuous variable.

Overall, the histogram is specifically designed to represent the distribution and frequency of data, making it the correct choice for that purpose.