Which of the following best explains why one graph appears skewed and one graph appears symmetric when visualizing data?

• A. The distribution of the data values in one dataset is not centered and has a longer tail on one side, while the other dataset’s values are evenly distributed around the center.
• B. The type of graph used automatically determines whether the data will appear skewed or symmetric, regardless of the data values.
• C. A graph appears symmetric only if all data values are identical.
• D. Skewness and symmetry are only properties of qualitative data, not quantitative data.

Answer: (A)

Verified step by step guidance

1. Understand the concept of skewness and symmetry in data distributions. Skewness refers to the asymmetry in the distribution of data values, where one tail is longer or fatter than the other, while symmetry means the data values are evenly distributed around a central point.
2. Recognize that the shape of a graph (such as a histogram or boxplot) reflects the underlying distribution of the data values, not the type of graph itself. The graph visually represents how data points are spread out.
3. Identify that a skewed graph occurs when the data distribution is not centered and has a longer tail on one side, indicating that values are more spread out in that direction.
4. Note that a symmetric graph appears when data values are evenly distributed around the center, meaning the left and right sides of the graph are roughly mirror images.
5. Conclude that skewness and symmetry are properties of quantitative data distributions and are determined by the actual data values, not by the graph type or whether data values are identical.