What kind of graph would help us to analyze the stability of a non-parametric distribution of data points?

• A. Bar Graph
• B. Box-Plot
• C. Line Graph
• D. Scatter Plot

Answer: (B)

A box-plot is particularly effective for analyzing the stability of a non-parametric distribution of data points because it visually summarizes key statistical features of the dataset, including the median, quartiles, and potential outliers. This graphical representation allows observers to easily identify the spread and skewness of the data, as well as any variability that might indicate instability.

Box-plots also effectively communicate the interquartile range, which provides insight into the data's dispersion. By displaying the spread of the middle 50% of the data, along with any extreme values, box-plots can highlight whether the data is tightly clustered or widely spread, which is essential in assessing stability in distributions that do not adhere to a normal distribution pattern.

In contrast, a bar graph primarily represents categorical data and is not suited for analyzing distribution characteristics. A line graph typically illustrates trends over time rather than stability in distribution. A scatter plot is useful for showing the relationship between two quantitative variables but does not specifically address distribution characteristics or stability. This context reinforces why the box-plot is the most appropriate choice for this type of analysis.