AP®︎ Statistics (pre-2026): Unit 1 Flashcards

Descriptive summarizes observed data; inferential uses sample data to generalize about a population.

A collection of related observations gathered for a statistical study.

The recorded value or values for one case in a data set.

Respondents answer surveys; subjects participate in experiments; experimental units are any units receiving treatments.

Common approaches include surveys, experiments, observations, and secondary sources for obtaining data.

The who, what, when, where, why, and how that make data meaningful.

Recorded information consisting of the observed values of variables for individuals, objects, or events.

An individual, object, or unit on which data are collected; also called an element or case.

A characteristic measured on each individual or case that can take different values.

A variable whose values are labels or group names rather than numbers.

A variable whose values are numerical counts or measurements.

Discrete quantitative variables take separate, countable values; continuous quantitative variables can take any value in an interval.

A category’s share of the total, written as a proportion, percent, or rate.

Use counts or proportions to compare categories and justify claims in context.

Organizes counts for two categorical variables in rows and columns, usually with marginal totals.

Use tables or graphs to compare counts or proportions for the same categories across groups.

Uses separated equal-width bars to show and compare category counts or relative frequencies.

Bar graphs compare categories clearly, while pie charts show each category's proportion of the whole.

Categorical graphs can mislead through truncated axes, distorted areas, poor scaling, or cluttered categories.

Tables that summarize categorical data by listing each category with its count (frequency) and/or proportion or percent (relative frequency).

A display splitting each value into a stem and leaf while preserving individual data values.

A graph placing one dot per observation above its value, stacking dots for repeated or close values.

A graph showing the number or proportion of observations less than or equal to each value.

A line graph connecting class midpoint frequencies to show a quantitative distribution.

A graph of quantitative data using adjacent interval bars whose heights show frequency or proportion.

Describe it by shape, center, spread, and unusual features like outliers, gaps, or clusters.

The left and right sides are approximately mirror images around the center.

Right-skewed has a longer right tail; left-skewed has a longer left tail.

One peak is unimodal, two prominent peaks are bimodal, and similar bar heights are approximately uniform.

A region between data values where no observations occur.

A concentration of data values, often separated from others by gaps.

Mean is the average, median is the middle ordered value, and mode is the most frequent value.

Range is max minus min, standard deviation measures typical distance from the mean, and IQR is Q3 minus Q1.

Numerical and graphical summaries that describe observed data without generalizing to a population.

A statistic summarizes sample data, while a parameter summarizes an entire population.

The sum of all data values divided by the number of values, x̄ = Σx/n.

The middle value in ordered data; for even n, usually the average of the two middle values.

The difference between the maximum and minimum values in a data set.

Standard deviation measures typical distance from the mean; its square, s², is the sample variance.

Adding or subtracting a constant shifts center measures; multiplying or dividing rescales both center and spread.

Median and IQR resist outliers; mean, standard deviation, and range are strongly affected by them.

Use the mean and standard deviation for roughly symmetric distributions without strong outliers; use the median and IQR for skewed distributions or distributions with outliers.

The difference between the third and first quartiles, Q3 - Q1; it measures the spread of the middle 50% of the data.

Minimum, Q1, median, Q3, and maximum values that summarize a quantitative dataset.

Lower fence is Q1 minus 1.5 IQR; upper fence is Q3 plus 1.5 IQR.

Use center, spread, shape, and outliers from graphs to support claims about real data.

Graph of the five-number summary with a box, median line, whiskers, and separate outliers.

Shape can be inferred from boxplots, and mean-median position helps identify symmetry or skew.

A value unusually small or large compared with the rest of the data. Possible outliers are often identified using the 1.5 IQR rule: values below Q1 - 1.5(IQR) or above Q3 + 1.5(IQR); on a boxplot, these are plotted separately.

Values that divide ordered data into four parts: Q1 is the median of the lower half, the median is the middle, and Q3 is the median of the upper half.

Compare whether distributions are symmetric, skewed, unimodal, or have clusters and gaps.

Right-skewed distributions usually have mean above median; symmetric ones have mean near median.

Compare groups by shape, center, spread, outliers, clusters, and gaps.

Histograms, stem plots, and side-by-side boxplots compare quantitative distributions across groups.

Use means, medians, range, IQR, or standard deviation to compare center and variability.

A numerical summary that describes a population, such as μ or σ.

About 68%, 95%, and 99.7% of values lie within 1, 2, and 3 standard deviations.

Use z-scores with a calculator, z-table, or software to find area under the curve.

Use inverse normal technology with a mean, standard deviation, and area to estimate a data value.

Adding or subtracting shifts center; multiplying or dividing rescales spread without changing shape.

Many real variables, like body temperature or loaf weight, can be approximated by a normal model.

A distribution that is roughly symmetric, unimodal, and mound-shaped, like a normal curve.

Its center is set by μ, spread by σ, and the standard model is N(0,1).

Measures of relative position used to compare observations within or between distributions.

Measures of relative position in a distribution. A z-score standardizes a value by subtracting the mean and dividing by the standard deviation, while a percentile is the value with a given percent of observations less than or equal to it.