Displaying Distributions with Graphs

Choosing the Right Graph

The type of graph depends on the type of data:

| Data Type | Appropriate Graphs | |-----------|-------------------| | Categorical | Bar graph, pie chart, two-way table | | Quantitative | Histogram, dotplot, stemplot, boxplot |

Bar Graphs and Pie Charts (Categorical Data)

Bar graphs display the frequency or relative frequency of each category. Bars should have equal width and gaps between them.

Pie charts show the proportion of each category relative to the whole. All slices must sum to 100%.

Histograms (Quantitative Data)

Histograms group data into bins (intervals of equal width). The height of each bar represents frequency or relative frequency.

Key features to describe:

• Shape: Symmetric, skewed left, skewed right, bimodal, uniform
• Center: Where the "middle" of the data falls
• Spread: Range from minimum to maximum
• Outliers: Unusual values

Dotplots

Each data point is represented by a dot above a number line. Best for small datasets.

Stemplots (Stem-and-Leaf Plots)

Each data value is split into a stem (leading digits) and leaf (trailing digit).

Example: For the data 23, 25, 31, 34, 37: $\text{Stem} | \text{Leaf}$ $2 | 3 \; 5$ $3 | 1 \; 4 \; 7$

Back-to-back stemplots compare two distributions.

Describing Shape

• Symmetric: Left and right sides are approximately mirror images
• Skewed right: Tail extends to the right (mean > median)
• Skewed left: Tail extends to the left (mean < median)
• Bimodal: Two peaks
• Uniform: Approximately equal frequencies

AP Tip: Always describe distributions using Shape, Outliers, Center, and Spread (SOCS).