The histogram is the most appropriate graphical representation for displaying frequencies of numerical discrete data because it effectively shows the distribution of that data across different intervals or bins. In a histogram, the x-axis represents the range of the numerical values while the y-axis indicates the frequency of observations within each interval. This allows for a clear visualization of how the data is spread out and for identifying patterns such as peaks, gaps, or outliers.
While bar charts are commonly used for displaying categorical data and comparing different groups, they can also represent discrete numerical data but do not provide the same level of detail regarding distribution as a histogram. Box plots are used to summarize the central tendency and variability of a dataset, highlighting medians and quartiles, but they lack clarity regarding the frequency of specific values or intervals. Pie charts are not suitable for representing discrete numerical data as they are typically used to show proportions of a whole for categorical data rather than the frequency of numerical values. Thus, for displaying frequencies of numerical discrete data, a histogram is the most effective tool, as it provides valuable insights into the data's distribution.