AP Statistics Unit 1: Exploring One-Variable Data and Collecting Data

Comprehensive vocabulary flashcards covering sampling methods, bias, study design, measures of center and spread, outlier criteria, and data displays from AP Statistics Unit 1.

Convenience Sample

A sampling method in which individuals who are easiest to reach are selected, frequently leading to under-representation of other population members and causing coverage bias.

Voluntary Response Sample

A sample consisting of individuals who choose themselves to participate in a survey, which typically suffers from non-response bias and over-represents people with strong opinions.

Coverage Bias (Under-coverage)

A type of selection bias that occurs when some groups or segments in the population are left out of or under-represented by the sampling process.

Non-Response Bias

A bias that occurs when individuals chosen or invited to be part of the sample fail or choose not to respond to the survey.

Leading Question

A survey question phrased or framed to prompt, influence, or argue for a specific response before asking for the respondent's opinion.

Choice Bias (Limited vs. Repeated)

A survey design flaw where question options either unnecessarily restrict possible answers (limited) or present overlapping response intervals such as $6-8$ and $8-10$ (repeated).

Interviewer Bias

A bias that occurs when characteristics or the presence of the interviewer influence the respondent to alter their true responses (such as answering favorably to please an authority figure).

Simple Random Sample (SRS)

A sampling design in which every individual in the population is assigned a unique label and selected via a random number generator such that every group of size $n$ has an equal chance of selection.

Systematic Sampling

A sampling method where individuals are ordered on a list and every $k\text{th}$ individual is selected after picking a random starting point between $1$ and $k$.

Stratified Random Sampling

A sampling method where a population is divided into homogeneous sub-groups (strata) based on a shared characteristic, and an independent SRS is taken from each stratum.

Cluster Sampling

A sampling method where the population is divided into heterogeneous groups (clusters) that each resemble the population, several entire clusters are randomly chosen, and all individuals within those clusters are surveyed.

Strata vs. Cluster Group Composition

Strata are homogeneous within each group and heterogeneous between groups, whereas clusters are heterogeneous within each group and homogeneous between groups.

Retrospective Study

An observational study that identifies subjects and collects data by looking backward in time at past events, behaviors, or historical records without imposing treatments.

Prospective Study

An observational study that identifies subjects in the present and follows them forward in time over an extended period to measure future outcomes without imposing treatments.

Experiment

A study design in which researchers deliberately impose specific treatments on experimental units to observe the responses and measure outcomes.

Single-Blind Experiment

An experimental procedure where the subjects do not know which treatment they are receiving, but the researcher administering the treatment does know.

Double-Blind Experiment

An experimental procedure where neither the subjects nor the individuals interacting with them and administering treatments know which treatment is being given.

Matched Pairs Design

A specialized block design in which each participant receives both treatments in a randomized order, or paired subjects with similar traits receive alternate treatments.

Sample Survey

A study that collects information and data from a subset (sample) of individuals to learn about the broader population.

Census

A complete enumeration or study that measures every single individual within an entire population.

Random Sampling vs. Random Assignment

Random sampling allows inferences to be generalized to the broader population, while random assignment allows researchers to make cause-and-effect inferences between variables.

Right-Skewed Distribution (Histogram)

A distribution shape where a majority of the data values are clustered at lower numbers on the left, with the tail stretching out toward larger values on the right.

Mean vs. Median (Resistance to Outliers)

The mean is non-resistant and pulls toward extreme values or outliers, whereas the median is resistant to extreme values because its position depends only on the rank order of data.

Interquartile Range (IQR)

A resistant measure of spread calculated as $\text{IQR} = Q_3 - Q_1$, measuring the range of the middle $50\%$ of ordered data values.

$z$-score

A standardized measure calculated as $z = \frac{x - \mu}{\sigma}$ that specifies the number of standard deviations a raw observation $x$ falls above or below the mean $\mu$.

Five-Number Summary

A numerical summary of quantitative data consisting of the Minimum, First Quartile ($Q_1$), Median ($\text{Med}$), Third Quartile ($Q_3$), and Maximum.

$1.5 \times \text{IQR}$ Outlier Rule

A criterion where data values are flagged as outliers if they fall below $\text{LB} = Q_1 - 1.5(\text{IQR})$ or above $\text{UB} = Q_3 + 1.5(\text{IQR})$.

Two-Standard-Deviation Outlier Rule

An outlier identification rule that flags any score falling outside the interval defined by $\text{LB} = \bar{x} - 2s$ and $\text{UB} = \bar{x} + 2s$.

Modified Boxplot

A boxplot where the whiskers extend only to the smallest and largest non-outlying observations, while outliers beyond the cutoff fences are plotted as individual points.

Histogram vs. Boxplot Informational Strengths

A histogram shows frequencies of observations within specific intervals, whereas a boxplot explicitly displays quartiles and identifies individual outliers.