What type of plot is used to show the distribution of a numerical value through probability density?

A violin plot is utilized to illustrate the distribution of a numerical value through probability density by combining a box plot's statistics with the density estimate of the data. It essentially shows the frequency of data at different values, providing insight into the shape of the distribution. The width of the 'violin' at various y-values indicates the density of the data points, highlighting where values are concentrated.

This dual representation allows for an easier and more informative visualization than simply using a box plot, as it can display multimodal distributions effectively, something other plot types do not do as comprehensively. The violin plot effectively summarizes the underlying distribution, making it particularly useful in exploratory data analysis, where understanding the full shape of the data distribution is crucial for making further inferences.

While histograms also show the distribution of numerical data, they do so using bins and might not present a smooth density estimate. Box plots provide summary statistics such as the median and interquartile range, but they do not convey the distribution's shape. Bar charts are generally used for categorical data rather than numerical distributions. In summary, the violin plot uniquely conveys both statistical and distributional information, which is why it is the correct choice for this question.