| name | descriptive-statistics |
| description | Summarizing and visualizing data through measures of center, spread, shape, and position. Covers mean, median, mode, range, IQR, variance, standard deviation, percentiles, z-scores, five-number summaries, and graphical displays (histograms, box plots, stem-and-leaf, dot plots, scatter plots). Emphasizes choosing the right summary for the data's shape and scale. Use when summarizing datasets, choosing visualizations, computing summary statistics, or interpreting distributions. |
| type | skill |
| category | statistics |
| status | stable |
| origin | tibsfox |
| modified | false |
| first_seen | "2026-04-11T00:00:00.000Z" |
| first_path | examples/skills/statistics/descriptive-statistics/SKILL.md |
| superseded_by | null |
Descriptive Statistics
Descriptive statistics distills raw data into interpretable summaries. Before any inference, modeling, or prediction, a dataset must be described: its center, its spread, its shape, and its notable features. This skill covers the full toolkit of numerical summaries and graphical displays that turn observations into understanding.
Agent affinity: pearson (measures of association), gosset (small-sample summaries), george (pedagogy)
Concept IDs: stat-descriptive-statistics, stat-data-visualization
Measures of Center
The center of a distribution answers "where is the typical value?"
| Measure | Definition | Best for | Sensitive to |
|---|
| Mean | Sum of values divided by count | Symmetric distributions | Outliers, skew |
| Median | Middle value when sorted | Skewed distributions, ordinal data | Nothing -- robust |
| Mode | Most frequent value | Categorical data, multimodal distributions | Ties, bin width |
| Trimmed mean | Mean after removing k% from each tail | Distributions with mild outliers | Choice of trim percentage |
Decision rule. Use the mean when the distribution is roughly symmetric with no extreme outliers. Use the median when the distribution is skewed or contains outliers. Use the mode for categorical data or when identifying the most common category matters more than a numeric center.
When they diverge. If mean and median differ substantially, the distribution is skewed. Mean > median indicates right skew (pulled by high values); mean < median indicates left skew. The distance between them is a rough skew indicator.
Measures of Spread
Spread answers "how variable are the values?"
| Measure | Definition | Best for | Properties |
|---|
| Range | Max minus min | Quick sense of total spread | Extremely sensitive to outliers |
| IQR | Q3 minus Q1 | Robust measure alongside median | Ignores tails entirely |
| Variance | Average squared deviation from the mean | Theoretical work, ANOVA | In squared units |
