Displaying and Describing Distributions

Types of variables

• Categorical: places individuals into groups (eye colour, favourite sport).
• Quantitative: numerical values where arithmetic makes sense (height, time).

Displays

Variable type	Displays
categorical	bar chart, pie chart, frequency table
quantitative	dotplot, stemplot, histogram, boxplot, cumulative graph

Describing a quantitative distribution: SOCS

• Shape: symmetric, skewed right (long tail to the right), skewed left; unimodal or bimodal.
• Outliers: values far from the rest.
• Center: median or mean.
• Spread: range, IQR or standard deviation.

Always describe in context: The distribution of commute times is skewed right with a median of 22 minutes; one student's 95-minute commute is a possible outlier.

Shape and center

• Skewed right: mean > median (the tail pulls the mean).
• Skewed left: mean < median.
• Roughly symmetric: mean ≈ median.

Comparing distributions

Compare shape, center, spread and outliers, using comparative words (greater than, about the same as), and mention both groups.

Quick summary

• Categorical vs quantitative determines the display.
• Describe shape, outliers, center and spread, in context.
• Skew pulls the mean toward the tail.