Chapter 1: Exploring Data Flashcards

Vocabulary terms and definitions from Chapter 1 regarding data individuals, variables, categorical analysis, and quantitative displays.

Individuals

The objects described by a set of data, which may be people, animals, or things.

Variable

Any characteristic of an individual that can take different values for different individuals.

Categorical Variable

A variable that places an individual into one of several groups or categories.

Quantitative Variable

A variable that takes numerical values for which it makes sense to find an average.

Distribution

Describes what values a variable takes and how often it takes these values.

Inference

The process of drawing conclusions that go beyond the data at hand.

Frequency Table

A table that displays the counts (frequencies) of individuals in each category.

Relative Frequency Table

A table that shows the percents (relative frequencies) of individuals in each category.

Roundoff Error

The discrepancy that occurs when percents are rounded to the nearest tenth and may not add exactly to $100\%$.

Pie Chart

A circular display showing the distribution of a categorical variable as slices sized by counts or percents; it must include all categories that make up a whole.

Bar Graph

A graph that represents each category as a bar, where heights show the category counts or percents.

Two-way Table

A table that describes two categorical variables, organizing counts by row and column variables.

Marginal Distribution

The distribution of values of one categorical variable in a two-way table among all individuals described by the table.

Conditional Distribution

Describes the values of a variable among individuals who have a specific value of another variable.

Segmented Bar Graph

A graph where each bar represents a category and contains segments representing the distribution of another variable within that category, with each bar reaching a total height of $100\%$.

Association

The relationship between two variables where specific values of one variable tend to occur in common with specific values of the other.

Simpson's Paradox

An association between two variables that holds for each individual value of a third variable but is changed or reversed when the data are combined.

Dotplot

A simple graph for quantitative data where each value is shown as a dot above its location on a number line.

Symmetric Distribution

A distribution where the right and left sides of the graph are approximately mirror images of each other.

Skewed to the Right

A distribution where the right side of the graph (containing the half of the observations with larger values) is much longer than the left side.

Skewed to the Left

A distribution where the left side of the graph is much longer than the right side.

Unimodal

A distribution with a single major peak.

Bimodal

A distribution with two clear peaks.

Stemplot

A graphical display for small sets of quantitative data that separates each observation into a stem and a leaf.

Histogram

A graph for quantitative variables that groups nearby values together into classes of equal width and displays heights as frequencies or relative frequencies.

Mean

The arithmetic average of a set of observations, calculated as $\bar{x} = \frac{\sum x_i}{n}$.

Median

The midpoint of a distribution such that half the observations are smaller and the other half are larger; denoted as $M$.

Resistant Measure

A statistical measure that is not sensitive to the influence of extreme observations or outliers.

Interquartile Range (IQR)

The range of the middle $50\%$ of the data, calculated as $IQR = Q_3 - Q_1$.

$1.5 \times IQR$ Rule

A rule of thumb for identifying outliers: an observation is an outlier if it falls more than $1.5 \times IQR$ above the third quartile or below the first quartile.

Five-Number Summary

Includes a distribution's Minimum, $Q_1$, Median, $Q_3$, and Maximum.

Boxplot

A graph based on the five-number summary where a central box spans the quartiles, a line marks the median, and whiskers extend to the smallest and largest non-outlier values.

Variance

The average squared distance of observations from their mean, calculated as $s_x^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1}$.

Standard Deviation

The square root of the variance, measuring the average distance of the observations from their mean; denoted as $s_x$.