Free-response Question 2: analyzing data and interpreting results

What the exam asks

Question 2 presents a real or hypothetical dataset—often with tables, summary statistics, or graphs such as boxplots, histograms, dotplots, or mosaic plots—and asks you to analyze and interpret the data across labeled parts (A, B, C, etc., often with subparts i and ii). Across its 10 points (each earned independently unless the scoring guideline says otherwise), you will typically be asked to:

• Identify or complete an appropriate graphical or tabular representation and explain why it fits the variable type.
• Calculate summary statistics, relative frequencies, $z$-scores, or outlier fences, showing your work.
• Describe or compare distributions of quantitative or categorical variables in context.
• Justify a claim or the choice of a summary statistic using specific numbers from the prompt or from your earlier answers.

Core ideas

Choosing and justifying representations

Match the graph or table to the variable type and the research goal, and state why it is appropriate:

• Categorical data: Use bar charts, relative frequency tables, or segmented bar charts / mosaic plots (for comparing two categorical variables). Relative frequencies (proportions or percentages) are required when comparing groups of unequal sample sizes.
• Quantitative data: Use histograms, dotplots, stem-and-leaf plots, or boxplots. Boxplots are ideal for quick side-by-side comparisons of medians, interquartile ranges ($IQR$), and outliers, whereas histograms and dotplots show more detail of shape, gaps, and clusters.

Showing calculation work in Bluebook

A bare number without supporting work rarely earns full credit. Always show an expression with substituted values and the final result:

• Outlier fences: State the $IQR = Q_3 - Q_1$, then substitute values into $Q_1 - 1.5(IQR)$ and , and explicitly compare the data minimum/maximum to the fences.

Use standard keyboard notation in the Bluebook response box so you do not waste time hunting through symbol menus:

Describing and comparing distributions

When describing or comparing quantitative distributions, address the four features (shape, center, variability and unusual features), all in context. The memory aid CUCS covers them: Center, Unusual features (outliers, gaps, clusters), Context (variable name, units, and groups), and Shape and Spread (variability).