1.5 Representing a Quantitative Variable with Graphs

Common Graphs for Quantitative Data

Dotplots, stemplots (stem-and-leaf), and histograms display distributions of quantitative variables. Dotplots stack dots for each value — great for small datasets. Stemplots split values into stems and leaves, preserving actual data. Histograms group data into intervals (bins) and show bar heights as frequency or relative frequency, best for larger datasets.

Describing Distributions: SOCS

Always describe distributions using Shape, Outliers, Center, Spread (SOCS). Shape can be symmetric, skewed left, skewed right, unimodal, bimodal, or uniform. Note any outliers (unusually far values). Center is a typical value (mean/median), and spread describes variability (range, IQR, standard deviation). Context matters — always relate back to the variable being measured!

Choosing Bin Width & Cumulative Graphs

In histograms, changing bin width changes the picture: too few bins hide detail, too many create noise. A cumulative relative frequency graph (ogive) plots running totals of percentages, useful for finding percentiles and describing position within a distribution. Always label axes and include units for full credit on the AP exam.

Key terms

Dotplot

A graph with dots stacked above a number line representing each data value; good for small datasets.

Stemplot

A graph splitting data into stems and leaves, preserving actual values while showing distribution shape.

Histogram

A graph grouping quantitative data into intervals (bins) with bar heights showing frequency or relative frequency.

SOCS

Shape, Outliers, Center, Spread — the key elements to include when describing a distribution.

Skewed distribution

A distribution with a longer tail on one side; named for the direction the tail points (left or right).

Try an AP-style question

In a stemplot with the key 2 | 5 = 25, what value does 4 | 7 represent?

1. 4.7
2. 74
3. 47
4. 407