SAT / PSAT
SAT / PSAT Prep
History & Social Science
AP World History AP US History AP European History AP Human Geography AP US Government & Politics AP Psychology AP Macroeconomics AP Microeconomics
English
AP English Language & Composition AP English Literature & Composition
Math & Computer Science
AP Calculus AB/BC AP Precalculus AP Statistics AP Computer Science A AP Computer Science Principles
Sciences
AP Biology AP Chemistry AP Environmental Science AP Physics 1 AP Physics 2
World Languages & Arts
AP Spanish Language AP Art History AP Music Theory Start studying →
Unit 1 · Exploring One-Variable Data & Collecting Data Flashcards Cheat Sheet Essentials Visual Review MC Practice FRQ Practice

AP Statistics Unit 1 Visual Review

A topic-by-topic visual walkthrough of Unit 1: Exploring One-Variable Data and Collecting Data — variables, graphs, summary statistics, sampling, and experimental design.

← Back to Unit 1 hub
TOPIC 1.1 What Can We Learn from Data? Statistics turns data into insight Data are values collected about individuals — but they always VARY. Statistics is the science of learning from data in the presence of that variability. A good investigative question A statistical question ANTICIPATES variability in the answers. "How tall are students here?" (varies) ✓ "How tall am I?" (one answer) ✗ The statistical process 1. Ask a question → 2. Collect data → 3. Analyze the data → 4. Draw a conclusion (in context). Every unit of this course is a step in this cycle. Statistics learns from data amid variability; good questions anticipate it. The Review Hub · AP Statistics Unit 1 TOPIC 1.2 Variables Categorical variables Values are LABELS / groups, not numbers you do arithmetic on. Examples: eye color, brand, yes/no, grade level (as a category). Summarize with counts & proportions. Quantitative variables NUMERICAL values you can do arithmetic on (mean, etc.). DISCRETE: countable (number of pets). CONTINUOUS: measured (height, time). Summarize with mean, median, SD. The variable type decides the tools A ZIP code looks numeric but is CATEGORICAL — you'd never average ZIP codes. Always ask what the number means. Categorical = labels; quantitative = numbers you do arithmetic on. The Review Hub · AP Statistics Unit 1 TOPIC 1.3 One Categorical Variable: Tables FREQUENCY TABLE — favorite fruit Apple1845% Banana1435% Cherry820% Total40100% Frequency vs. relative frequency FREQUENCY = the count in each category. rel. freq = count / total Relative frequency = the PROPORTION (a %), useful for comparing groups. 18/40 = 0.45 = 45% Proportions add to 1 (100%) Relative frequencies of a single categorical variable always sum to 100% — a quick check on your table. Summarize a category with counts and relative frequencies (count/total). The Review Hub · AP Statistics Unit 1 TOPIC 1.4 One Categorical Variable: Graphs AppleBananaCherry bar chart (bars have gaps) Bar charts & pie charts BAR CHART: bar height = count or percent. Bars have GAPS (categories are separate). PIE CHART: slices show parts of a whole. Describe what you see Name the most/least common category and compare their frequencies IN CONTEXT. Bar order can be sorted for a cleaner display. Show categories with bar charts (gaps) or pie charts. The Review Hub · AP Statistics Unit 1 TOPIC 1.5 One Quantitative Variable: Graphs histogram (bars touch) value (binned) → Graphs for numbers HISTOGRAM: bars over intervals, TOUCHING (the scale is continuous). Also: dotplot, stemplot, boxplot. Histogram vs. bar chart Histogram = QUANTITATIVE, bars TOUCH. Bar chart = CATEGORICAL, bars have GAPS. Bin width changes the histogram's appearance. Show quantitative data with a histogram (touching bars), dotplot, or stemplot. The Review Hub · AP Statistics Unit 1 TOPIC 1.6 Describing a Distribution Describe SHAPE, CENTER, SPREAD — and OUTLIERS (in context) Always mention all four when describing a quantitative distribution, and tie them to the real variable. "SOCS": Shape, Outliers, Center, Spread. Shape symmetric skewed right Center & spread CENTER: mean or median. SPREAD: range, IQR, or SD. Skewed → use MEDIAN + IQR. Symmetric → use MEAN + SD. Skew pulls the mean Right-skew: mean > median. Left-skew: mean < median. The mean chases the tail; the median resists it. Describe Shape, Center, Spread, Outliers — skew pulls the mean toward the tail. The Review Hub · AP Statistics Unit 1 TOPIC 1.7 Summary Statistics // key formulas (on the AP formula sheet) mean x̄ = (Σxᵢ) / n std dev s = √( Σ(xᵢ − x̄)² / (n − 1) ) IQR = Q3 − Q1 range = max − min Resistant vs. non-resistant MEDIAN & IQR resist outliers. MEAN & SD are pulled by outliers. Use resistant measures for skewed data. Worked example Data 2, 4, 6, 8, 10: x̄ = 30/5 = 6. s ≈ 3.16, median = 6, IQR = 8 − 4 = 4. n − 1 in the SD denominator (sample SD). x̄=Σx/n, s=√(Σ(x−x̄)²/(n−1)), IQR=Q3−Q1; median & IQR resist outliers. The Review Hub · AP Statistics Unit 1 TOPIC 1.8 Boxplots & the Five-Number Summary minQ1medianQ3maxoutlier The 1.5 × IQR outlier rule outlier if x < Q1 − 1.5·IQR or x > Q3 + 1.5·IQR The five-number summary is min, Q1, median, Q3, max. The box spans the IQR; whiskers reach the last non-outlier. Boxplot shows the 5-number summary; outliers are beyond Q1/Q3 ± 1.5·IQR. The Review Hub · AP Statistics Unit 1 TOPIC 1.9 Comparing Distributions Compare, don't just describe When comparing two groups, use COMPARATIVE language: "Group A's median is HIGHER THAN B's." Compare shape, center, spread, outliers — explicitly, for BOTH groups. Good tools for comparison • SIDE-BY-SIDE boxplots • Back-to-back stemplots • Histograms on the SAME scale Same axis scale makes fair comparison possible. Always answer in context A common FRQ loses points for describing groups separately instead of COMPARING them with words like "greater/less." Use comparative language for shape, center, spread & outliers of both groups. The Review Hub · AP Statistics Unit 1 TOPIC 1.10 Data Collection Population vs. sample POPULATION: the entire group of interest. SAMPLE: the subset we actually study. A PARAMETER describes the population; a STATISTIC describes the sample. parameter μ, p ← estimated by → statistic x̄, p̂ Census vs. sample A CENSUS measures everyone — often too costly or impossible. A well-chosen sample lets us GENERALIZE to the population — if it's random. How we collect data decides what we can conclude. Sampling vs. experiments Random SAMPLING → generalize to a population. Random ASSIGNMENT (experiment) → establish cause and effect. A parameter (μ, p) describes a population; a statistic (x̄, p̂) describes a sample. The Review Hub · AP Statistics Unit 1 TOPIC 1.11 Random Sampling Four random sampling methods • SRS: every group of size n equally likely. • STRATIFIED: split into similar strata, SRS within each (boosts precision). • CLUSTER: split into groups, randomly pick whole clusters. • SYSTEMATIC: pick every k-th individual from a random start. Randomness avoids bias & allows inference. Why randomize? Random selection makes the sample REPRESENTATIVE in the long run and removes human selection bias. Only random samples justify generalizing results to the whole population. Stratified reduces variability by grouping similar individuals together. Larger samples shrink sampling variability. Random sampling (SRS, stratified, cluster, systematic) avoids bias & enables inference. The Review Hub · AP Statistics Unit 1 TOPIC 1.12 Potential Problems with Sampling Sources of bias • UNDERCOVERAGE: some groups left out. • NONRESPONSE: selected people don't reply. • RESPONSE bias: untruthful/leading Qs. • VOLUNTARY response: only strong opinions. • CONVENIENCE: easiest-to-reach people. Bias ≠ variability BIAS = systematically off in one direction. A bigger sample does NOT fix bias. VARIABILITY = spread of estimates; a larger sample DOES reduce it. Fix bias with better METHOD, not more data. Name the bias AND its direction On the exam: identify the type of bias and say whether it makes the estimate too HIGH or too LOW. Bias is systematic error a bigger sample can't fix; it only reduces variability. The Review Hub · AP Statistics Unit 1 TOPIC 1.13 Experimental Design Four principles • CONTROL other variables (comparison). • RANDOM ASSIGNMENT to treatments. • REPLICATION (enough subjects). • BLOCKING (group similar units, like stratifying) when useful. Key vocabulary TREATMENT: what's applied to a group. CONTROL group / PLACEBO: baseline. BLIND: subjects don't know their group; DOUBLE-BLIND: evaluators don't either. CONFOUNDING: a variable tangled with the treatment. Random assignment → causation Only a randomized comparative EXPERIMENT can establish cause and effect. Observational studies only show association. Experiments use control, random assignment, replication — random assignment proves causation. The Review Hub · AP Statistics Unit 1
1 / 13

How to use the visual review

Spend 30 seconds per slide before clicking next. Look at the graph, then ask yourself: "Could I describe this distribution with SOCS, or name this sampling method, from memory?"

Use the fullscreen button () on desktop for the best experience. Use arrow keys to navigate. Tap "Show all slides" to jump around.

This is great for review the night before the exam — fast, visual, and covers every display and idea you need to recognize in Unit 1.