STAT 2600: Descriptive Statistics and Data Visualization Review

Comprehensive vocabulary flashcards covering descriptive statistics, data visualization aesthetics, contingency tables, correlation, and regression concepts from STAT 2600 Homework 5 and Homework 6.

Measure of Centrality

A descriptive summary statistic that identifies the center or typical value of a data distribution, specifically including the mean, median, and mode, but excluding extreme values like the minimum or maximum.

Median

The middle value of an ordered dataset, which divides the distribution into two equal halves; it is mathematically equivalent to the $0.50$ quantile and the $50\text{th}$ percentile.

Measure of Dispersion

A summary statistic that quantifies the spread, variability, or dispersion of data points in a distribution, such as standard deviation, variance, and range, as distinguished from distribution shape or modality.

Interquartile Range (IQR)

A robust measure of statistical dispersion representing the range of the middle $50\%$ of ordered data, calculated as $IQR = Q_3 - Q_1$.

Outlier Criterion (1.5 × IQR Rule)

A standard rule identifying any data point as an outlier if it falls below the lower fence $Q_1 - 1.5 \times IQR$ or above the upper fence $Q_3 + 1.5 \times IQR$.

Visual Aesthetic

A visual property or graphical attribute—such as position, color, fill, shape, or size—mapped to a variable in order to represent data values visually.

Word Cloud

A text-based data visualization where the frequency or prominence of individual words within a written text is mapped to font size as its primary visual aesthetic.

Logarithmic Scale

A nonlinear axis scale based on orders of magnitude or powers of ten (e.g., $0.01$, $0.10$, $1.00$, $10.00$) useful for visualizing continuous numerical variables spanning multiple orders of magnitude.

Baseline Rule for Bar Charts

The data visualization standard requiring the quantitative axis displaying frequencies or counts in a categorical bar chart to begin at zero to maintain accurate visual proportionality.

Bar Chart vs. Histogram

A bar chart depicts the frequencies or counts of distinct levels for a categorical variable, whereas a histogram depicts the frequencies of values grouped into continuous interval bins for a numerical variable.

Bimodal Distribution

A distribution shape characterized by two distinct, clearly separated peaks of high frequency across its range.

Histogram Binning Limitation

The property of histograms that aggregates individual continuous observations into intervals, making it impossible to determine the frequency of an exact single value directly from the plot.

Box Plot

A graphical representation of the five-number summary showing the minimum, first quartile ($Q_1$), median ($Q_2$), third quartile ($Q_3$), and maximum, where the central box width depicts the interquartile range.

scale_x_continuous()

A ggplot2 layering function used to configure continuous horizontal axis properties, such as setting minimum and maximum limits or defining increment breaks.

Heat Map

A two-dimensional visualization technique where matrix cells defined by categorical groupings and/or time intervals display values mapped onto a continuous color gradient.

Contour Plot

A graphical method that projects the continuous value of a third variable or statistic onto a two-dimensional grid defined by two numerical variables using isolines or shaded regions.

Topographic Contour Interval

The vertical elevation change between successive contour lines on a map, used to evaluate whether traveling between two coordinates proceeds uphill, downhill, or level.

Marginal Proportion

In a contingency table, the proportion of total observations belonging to a single category of one variable, found by dividing a row or column marginal total by the overall table grand total.

Conditional Proportion

The proportion of observations possessing a given characteristic within a restricted subgroup, calculated by dividing the specific cell frequency by that subgroup's marginal total.

Joint Proportion

The proportion of observations across an entire dataset that simultaneously satisfy two specific conditions, calculated by dividing a single cell value by the table grand total.

Standardized Stacked Bar Chart

A stacked bar chart where each bar is scaled to $100\%$, allowing direct visual comparison of conditional proportions across different categorical groups regardless of sample size differences.

Evaluating Categorical Association

The procedure of checking independence between two categorical variables by comparing subgroup conditional proportions against the overall marginal proportion of that outcome.

Correlation Coefficient ($r$)

A standardized measure ranging from $-1$ to $+1$ that indicates the direction and strength of the linear relationship between two continuous numerical variables.

Nonlinear Association

A relationship between two quantitative variables visible in a scatter plot where data follow a curved trajectory (such as early growth that levels off) rather than a straight line.

Ordinary Least Squares (OLS) Regression

A linear modeling method that determines the straight line best fitting bivariate numerical data by minimizing the sum of the squared vertical differences between observed and predicted values.

Interpretation of Regression Slope

The expected (average predicted) change in the response variable ($y$) for every one-unit increase in the predictor variable ($x$), which represents an expected trend rather than a guaranteed outcome.