What problem-solving tool is best used to depict the frequency distribution of data using a vertical bar chart?

The histogram is the most effective tool for depicting the frequency distribution of data because it uses vertical bars to represent the number of occurrences (or frequency) of data points within specified ranges, known as bins. Each bar's height correlates with the frequency of data within that bin, allowing for a clear visual representation of how data is distributed across different intervals.

This method is particularly useful for understanding the shape and spread of the data distribution, as it highlights trends and patterns, such as whether data is normally distributed, skewed, or contains outliers. The use of vertical bars provides an intuitive way to compare different intervals and grasp the overall data trends at a glance.

In contrast, the other tools mentioned serve different purposes. A pie chart is designed to show proportional relationships, a line graph is used to illustrate trends over time, and a scatter plot displays the relationship between two variables without focusing on frequency distribution in bins. Therefore, none of these alternatives provide the same detailed visualization of data distribution that a histogram does.