AP Stats Unit 1: Data Types, Graphs, and Distributions

Categorical (Qualitative)

Describes groups or labels

Examples of Categorical Data

Gender, color, brand

Graphs for Categorical Data

Bar graph, pie chart, segmented bar chart

Quantitative (Numerical)

Describes amounts

Examples of Quantitative Data

Height, score, time

Graphs for Quantitative Data

Dotplot, histogram, boxplot

Two-Way Tables

Displays two categorical variables

Relative Frequency

Proportion or percent

Row Relative Frequency

Compare across rows

Column Relative Frequency

Compare down columns

Misleading Graphs

Y-axis does not start at 0, uneven or stretched scales, wrong graph type, 3D effects

Categorical Displays

Bar Graph → frequencies or percents

Pie Chart

Parts of a whole

Segmented Bar Chart

Relative frequencies by group

Association (Categorical Variables)

Variables are associated if conditional relative frequencies differ

Distribution Shapes (Quantitative)

Symmetric → mean ≈ median

Skewed Right Distribution

Tail right, mean > median

Skewed Left Distribution

Tail left, mean < median

Uniform Distribution

Roughly equal frequencies

Describing Distributions (SOCV)

S - Shape, O - Outliers, C - Center, V - Variability

Standard Deviation (SD)

Measures spread around the mean

Properties of Standard Deviation

Always ≥ 0, affected by outliers

1.5 × IQR Rule

Lower: Q1 − 1.5(IQR), Upper: Q3 + 1.5(IQR)

Effect of Outliers

Mean & SD nonresistant, Median & IQR resistant