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Unit 1 · Exploring One-Variable Data & Collecting Data Flashcards Cheat Sheet Essentials Visual Review MC Practice FRQ Practice

AP Statistics Unit 1 Essentials

The must-know terms and core concepts for Unit 1: Exploring One-Variable Data & Collecting Data. Every vocabulary word and idea you need to master.

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Key Concept 1
Statistics is a four-step investigative process
Every statistical study follows the same arc: formulate a question, collect data, analyze the data, and interpret the results. Unit 1 introduces all four steps. Recognizing where a problem sits in this process tells you what to do next — and the AP Exam constantly asks you to move between posing questions, choosing methods, computing, and drawing conclusions in context.
Investigative Process Data Interpretation
Key Concept 2
Describe one-variable data by type, then by shape, center, and spread
The first question about any variable is whether it is categorical or quantitative, because that determines the right display (bar and pie charts vs. dotplots, stemplots, and histograms) and the right statistics. For a quantitative distribution, describe it with SOCS — shape, outliers, center, and spread — and choose statistics wisely: the median and IQR are resistant to outliers, while the mean and standard deviation are not. The 1.5 × IQR rule gives an objective definition of an outlier.
Variable Types Distributions Resistant Statistics
Key Concept 3
How you collect data determines what you can conclude
A beautiful analysis of bad data is still worthless. Random sampling (simple random, stratified, cluster, systematic) is what lets you generalize a sample's results to a population, and avoiding bias — undercoverage, nonresponse, response bias, voluntary response — keeps those results trustworthy. To claim cause and effect, you need an experiment with random assignment; an observational study can only show association because of possible confounding.
Sampling Bias Experiments
Individual
A single member of a population or sample for which data are recorded; an observational unit.
Data Basics
Variable
A characteristic recorded for each individual, whose values vary among individuals.
Data Basics
Categorical variable
A variable that places each individual into a group or category.
Data Basics
Quantitative variable
A variable that takes numerical values for which arithmetic is meaningful.
Data Basics
Distribution
The pattern of the values a variable takes and how frequently each value occurs.
Data Basics
Frequency / relative frequency
A count within a category, and that count as a proportion or percent of the whole.
Categorical
Bar chart
A display of a categorical variable using separated bars whose heights show frequency or relative frequency.
Categorical
Histogram
A display of a quantitative variable using touching bars over equal-width intervals.
Quantitative Graphs
Dotplot / stemplot
Displays that show each value of a small quantitative data set individually.
Quantitative Graphs
Shape
The overall form of a distribution: symmetric, skewed left, skewed right, uniform, or bimodal.
Describing
Skewness
A lack of symmetry; the distribution has a longer tail on one side, which pulls the mean toward it.
Describing
Outlier
An unusually large or small value; by the 1.5 × IQR rule, one beyond Q1 − 1.5·IQR or Q3 + 1.5·IQR.
Describing
Mean
The arithmetic average of a set of values; not resistant to outliers.
Summary Statistics
Median
The middle value of ordered data; resistant to outliers.
Summary Statistics
Range / IQR
Max − min, and Q3 − Q1 (the spread of the middle 50%); the IQR is resistant.
Summary Statistics
Standard deviation
The typical distance of values from the mean; larger means more spread. Not resistant.
Summary Statistics
Five-number summary
Minimum, Q1, median, Q3, maximum — the basis of a boxplot.
Summary Statistics
Percentile
The value at or below which a given percent of the data fall.
Summary Statistics
Population / sample
The entire group of interest, and the subset actually studied.
Collecting Data
Parameter / statistic
A number describing a population (usually unknown) vs. a number computed from a sample.
Collecting Data
Simple random sample (SRS)
A sample in which every group of n individuals is equally likely to be chosen.
Collecting Data
Stratified / cluster sampling
Sampling within similar strata, vs. randomly selecting whole clusters.
Collecting Data
Bias
A systematic tendency to over- or under-estimate the truth, from flawed sampling or design.
Collecting Data
Experiment / observational study
A study that imposes treatments (allowing cause and effect with random assignment) vs. one that only measures.
Collecting Data
Confounding
When the effects of two variables on the response cannot be distinguished.
Collecting Data