Final answer:
A histogram is the most appropriate graphical display for analyzing the distribution of students' test scores. It clearly shows frequency distributions for continuous data, like test scores, and allows for the identification of distribution shapes, clusters, gaps, and possible outliers.
Step-by-step explanation:
In analyzing the distribution of students' test scores, the most appropriate graphical display would be a histogram. A histogram is useful for showing the frequency of score ranges and provides a clear visualization of how the scores are distributed across different intervals. This is particularly valuable for continuous, quantitative data such as test scores. Bar graphs could be used for discrete data, a scatter plot is best for showing relationships between two variables, and a pie chart is suitable for displaying parts of a whole for categorical data. In the context of test scores, the histogram allows us to see where clusters of scores occur, if there are any gaps in the data, and if the distribution is symmetric, skewed, or has outliers.
For example, the histogram may show a concentration of scores in the 70-80 range, suggesting that a large number of students performed within this bracket. If the histogram shows a long tail to the left, it indicates that fewer students had lower scores, which could signify a left-skewed distribution. In comparing the graphical representations, the ease of interpretation and the specific types of data they are designed to present make histograms the best choice for illustrating test score distributions in a quantitatively meaningful way