Every term below is defined the way it is actually used in chart interpretation. Terms link to the tool where you can see each concept in action.
Central Tendency
- Mean
- The arithmetic average: sum of values divided by count. Sensitive to outliers.
- Median
- The middle value of sorted data (50th percentile). Robust to outliers.
- Mode
- The most frequent value. A distribution can have zero, one, or several modes.
- Trimmed Mean
- The mean after dropping a fixed percentage of extremes from both ends.
Spread
- Range
- Max minus min. Simple, but entirely determined by the two most extreme values.
- Quartiles (Q1, Q2, Q3)
- Values splitting sorted data into quarters. Q2 is the median.
- IQR (Interquartile Range)
- Q3 − Q1; the spread of the middle 50% and the width of a box plot's box.
- Variance
- The average squared deviation from the mean (σ²).
- Standard Deviation
- The square root of variance — spread in the same units as the data.
- MAD
- Median absolute deviation from the median; a fully robust spread measure.
- Coefficient of Variation
- SD ÷ mean; spread relative to scale, useful for comparing unlike datasets.
Distribution Shape
- Normal Distribution
- The symmetric bell curve defined by mean and SD; basis of many statistical tests.
- Skewness
- Asymmetry. Positive = long right tail; negative = long left tail.
- Kurtosis
- Tail heaviness. High kurtosis means more extreme values than a normal curve.
- Modality
- Number of peaks: unimodal, bimodal, multimodal. Visible in histograms and violin plots, invisible in box plots.
- Percentile / Quantile
- The value below which p% of the data falls; quantile is the 0–1 fraction version.
- KDE (Kernel Density Estimation)
- Smoothed estimate of a distribution's density curve; the engine behind violin plots.
- Bandwidth
- KDE's smoothing parameter — small is wiggly, large is smooth.
Outliers and Robustness
- Outlier
- A value far enough from the bulk of the data to warrant individual investigation.
- Tukey Fences
- Outlier boundaries at Q1 − 1.5×IQR and Q3 + 1.5×IQR.
- Z-Score
- (x − mean) / SD — how many standard deviations a value is from the mean.
- Masking
- When outliers inflate the mean/SD so much that they escape Z-score detection.
- Robust Statistic
- One barely affected by extreme values — median, IQR, MAD.
- Leverage Point
- An extreme X value that can dominate a regression slope.
Relationships and Testing
- Correlation (r)
- Strength and direction of a linear relationship, from −1 to +1.
- R² (Coefficient of Determination)
- Share of Y's variance explained by a linear model — 0 to 1.
- OLS Regression
- Ordinary least squares: the line minimizing squared vertical residuals.
- Q-Q Plot
- Quantile-quantile plot comparing sample quantiles to a theoretical distribution.
- Shapiro–Wilk Test
- A formal hypothesis test of normality; companion to the Q-Q plot.
- Five-Number Summary
- Min, Q1, median, Q3, max — everything a box plot encodes.
- Frequency Distribution
- Counts of observations per value range — the data behind every histogram.
- Bin (Class Interval)
- One range of values grouped for counting in a histogram.
- Freedman–Diaconis Rule
- Bin width = 2 × IQR × n^(−1/3); a robust automatic binning formula.