UC A-G Section CMathematicsWASC AccreditedHonors Course

Statistics / Honors Data Analysis
Think With Data

Data, Inference, Decisions

The most comprehensive agentic Honors Statistics course. From exploring data to statistical inference — master every analysis type, develop data science skills, and communicate findings with confidence — guided by Prof. Nadia Osei and SofAI.

Start with Prof. Nadia

All Courses

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Honors

Course Structure

Four Course Pillars

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Describe · Compare · Visualize

Exploratory Data Analysis

25%

› Categorical vs. quantitative variables and graphical displays
› Describing distributions using SOCS: Shape, Outliers, Center, Spread
› Scatterplots, correlation, and bivariate data patterns

Prof. Nadia's Tip: For every distribution, describe SOCS in order: Shape, Outliers, Center, Spread. Always include context — say 'commute times' not just 'values.'

🎲

Rules · Random Variables · Normal

Probability & Distributions

25%

› Basic probability rules and conditional probability
› Binomial and geometric distributions
› Central Limit Theorem and sampling distributions

Prof. Nadia's Tip: Name your distribution before calculating. 'X follows a Binomial distribution with n = 10, p = 0.4' earns the setup point before any computation.

🎯

Confidence Intervals · Significance Tests

Statistical Inference

30%

› Confidence interval structure: statistic ± critical value × SE
› Four-step hypothesis test: Hypotheses, Conditions, Calculations, Conclusion
› z-tests, t-tests, and chi-square tests of independence

Prof. Nadia's Tip: Always define your parameter first: 'Let p = the true proportion of all students who…' Then check Random, Normal, Independent conditions before calculating.

📈

LSRL · Residuals · Inference for Slope

Regression & Association

20%

› Least-squares regression line and interpreting slope and intercept
› Residuals and residual plots for checking linearity
› r² interpretation and inference for regression slope

Prof. Nadia's Tip: When interpreting slope: 'For each additional [x-unit], the predicted [y-variable] increases/decreases by [slope] [y-units] on average.' Always in context.

What You Will Build

Four Mastery Areas

Honors Statistics develops four interconnected skill sets that form the foundation of data science, research, and quantitative reasoning at the college level.

🧠

Statistical Thinking

Frame questions statistically, distinguish causation from association, and recognize when data supports a claim.

📉

Data Visualization

Create and interpret histograms, boxplots, scatterplots, and two-way tables to reveal patterns in data.

🎲

Probability Reasoning

Apply probability rules, model random phenomena with distributions, and use the Normal curve fluently.

🔬

Inference Skills

Construct confidence intervals, conduct significance tests, and communicate conclusions in context with evidence.

Honors Course Goals

Skills and outcomes you will demonstrate

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Describe and compare distributions using the full SOCS framework in every analysis

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Apply probability rules and distributions to model real-world random phenomena

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Conduct complete inference procedures with conditions checked and conclusions in context

✏️

Communicate findings in writing — every statistical claim supported by evidence and context

Full Curriculum

Eight Statistics Units

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UNIT 115-23%

Exploring One-Variable Data

Expand ›

Key Topics

Categorical vs. quantitative variables
Describing distributions: shape, center, spread, outliers (SOCS)
Measures of center: mean, median; measures of spread: range, IQR, standard deviation
Boxplots, histograms, dotplots, stemplots; comparing distributions

Key Terms

distribution

pattern of values: shape, center, spread of a variable

IQR

interquartile range = Q3 - Q1 (middle 50% spread)

outlier

value more than 1.5×IQR beyond Q1 or Q3

skewed right

tail extends to the right; mean > median

standard deviation

typical distance of values from the mean

z-score

number of standard deviations a value is from the mean: z = (x - μ)/σ

Practice Prompt

A dataset shows commute times (in minutes) for 20 workers: 12, 15, 18, 20, 20, 22, 25, 25, 28, 30, 30, 32, 35, 40, 45, 50, 55, 60, 75, 90. Calculate the mean, median, Q1, Q3, and IQR. Identify any outliers. Describe the distribution using SOCS. Would you use mean or median to describe center? Justify.

Practice with Prof. Nadia →

Curated Video Lessons

content

Describing Distributions — AP Statistics

Starnes AP Stats12 min

visual

Boxplots and Histograms

Khan Academy10 min

concept

Mean vs. Median — When to Use Which

AP Stats Guy8 min

📈

UNIT 25-7%

Exploring Two-Variable Data

Expand ›

Key Topics

Scatterplots: direction, form, strength, outliers
Correlation coefficient r: strength and direction (-1 to 1)
Least-squares regression line: ŷ = a + bx
Residuals = observed - predicted; residual plots for linearity check
Influential points vs. outliers in regression

Key Terms

correlation (r)

measures strength and direction of linear association (-1 to 1)

least-squares regression

line that minimizes sum of squared residuals

residual

observed y minus predicted ŷ

extrapolation

predicting outside the range of data (unreliable)

lurking variable

third variable causing the association between two others

coefficient of determination r²

% of variation in y explained by linear relationship with x

Practice Prompt

A researcher finds r = 0.87 between hours studied and test score. Write 3 correct interpretations of this r value. Then: what is r²? What does it mean in context? If the LSRL is ŷ = 42 + 5.3x (where x = hours studied), predict the test score for a student who studied 8 hours. A student studied 8 hours and scored 78. Calculate and interpret their residual.

Practice with Prof. Nadia →

Curated Video Lessons

content

Scatterplots and Correlation

AP Stats Guy11 min

content

LSRL — Least Squares Regression

Khan Academy AP Stats13 min

application

Residuals and Residual Plots

Starnes AP Stats9 min

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UNIT 312-18%

Collecting Data

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Key Topics

Census vs. sample; sampling methods (SRS, stratified, cluster, systematic)
Sources of bias: voluntary response, convenience, undercoverage, nonresponse
Observational studies vs. experiments
Experimental design: treatments, control, random assignment, placebo, double-blind
Confounding variables and how to control them

Key Terms

SRS

simple random sample — every individual has equal chance of selection

stratified random sample

divide into strata, then SRS from each stratum

confounding variable

variable that is related to both the explanatory and response variables

control group

group that receives no treatment (or placebo)

random assignment

randomly assigning subjects to treatments — eliminates confounding

double-blind

neither subjects nor evaluators know who received which treatment

Practice Prompt

A school wants to know if students prefer online or in-person learning. (a) Describe how to conduct a stratified random sample by grade level with n=120. (b) A student suggests using a voluntary response survey posted on the school website. Explain two sources of bias this introduces. (c) Design a randomized comparative experiment to test whether online tutoring improves test scores compared to in-person tutoring. Include: subjects, treatments, random assignment, and response variable.

Practice with Prof. Nadia →

Curated Video Lessons

content

Sampling Methods — AP Statistics

AP Stats Guy12 min

content

Experimental Design

Khan Academy AP Stats11 min

application

Bias in Surveys — AP Stats

Starnes AP Stats8 min

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UNIT 410-20%

Probability

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Key Topics

Basic probability rules: P(Aᶜ), P(A or B) = P(A) + P(B) - P(A and B)
Conditional probability: P(A|B) = P(A and B)/P(B)
Independent vs. mutually exclusive events
Venn diagrams and two-way tables
Law of Large Numbers and the Multiplication Rule

Key Terms

sample space

set of all possible outcomes

complement

P(Aᶜ) = 1 - P(A)

mutually exclusive

events that cannot both occur: P(A and B) = 0

independent events

P(A|B) = P(A): knowing B doesn't change probability of A

conditional probability

P(A|B) = P(A and B) / P(B)

Bayes' theorem

P(A|B) = P(B|A)·P(A) / P(B)

Practice Prompt

In a survey of 200 students, 120 play a sport and 80 are in band. 40 do both. (a) Create a two-way table. (b) Find P(Sport and Band), P(Sport or Band), P(Sport|Band), P(Band|Sport). (c) Are playing a sport and being in band independent? Show your work mathematically. (d) If 3 students are randomly selected without replacement, what is the probability all 3 play a sport?

Practice with Prof. Nadia →

Curated Video Lessons

content

Probability Rules — AP Statistics

AP Stats Guy10 min

content

Conditional Probability and Independence

Khan Academy AP Stats12 min

practice

Two-Way Tables and Conditional Probability

Starnes AP Stats9 min

📉

UNIT 57-12%

Random Variables and Probability Distributions

Expand ›

Key Topics

Discrete random variables: mean (μ), standard deviation (σ)
Continuous random variables and the Normal distribution
Binomial distribution: n trials, probability p of success, X ~ B(n,p)
Geometric distribution: number of trials until first success
Linear combinations of random variables: E(aX + b), Var(aX + b)

Key Terms

expected value E(X)

mean of a probability distribution: Σx·P(x)

binomial distribution

counts successes in fixed n independent trials with constant p

geometric distribution

counts trials until first success

Normal distribution

symmetric bell curve defined by μ and σ

standardizing

z = (X - μ)/σ — converts to standard normal

10% condition

sample < 10% of population — allows treating as independent

Practice Prompt

A student guesses on a 10-question true/false quiz. Let X = number correct. (a) Describe the distribution of X. (b) Find P(X ≥ 7). (c) Find the mean and standard deviation of X. (d) Now assume the quiz has 100 questions. What is the approximate probability the student gets more than 60 correct? Use the Normal approximation (check conditions first).

Practice with Prof. Nadia →

Curated Video Lessons

content

Discrete Random Variables — Expected Value

AP Stats Guy11 min

content

Binomial Distribution — AP Statistics

Khan Academy AP Stats14 min

visual

Normal Distributions and Z-Scores

Starnes AP Stats12 min

📐

UNIT 67-12%

Sampling Distributions

Expand ›

Key Topics

Sampling distribution of x̄: mean = μ, SD = σ/√n
Central Limit Theorem: x̄ approximately Normal when n ≥ 30
Sampling distribution of p̂: mean = p, SD = √(p(1-p)/n)
When to use z vs. t: known σ → z; unknown σ (use s) → t
Standard error vs. standard deviation

Key Terms

sampling distribution

distribution of a statistic over all possible samples of same size

Central Limit Theorem

x̄ is approximately Normal for large n, regardless of population shape

standard error

standard deviation of a sampling distribution

p̂ (p-hat)

sample proportion = count of successes / n

unbiased estimator

statistic whose mean equals the population parameter

variability

spread of a sampling distribution — decreases as n increases

Practice Prompt

The heights of adult women are Normally distributed with μ = 64 inches and σ = 2.8 inches. (a) What is the probability that one randomly selected woman is taller than 67 inches? (b) What is the sampling distribution of x̄ for samples of size n = 25? (c) What is the probability that the mean height of 25 women exceeds 65 inches? (d) If instead of height, we measured a heavily skewed variable (income), would the CLT still apply for n = 25? For n = 100? Explain.

Practice with Prof. Nadia →

Curated Video Lessons

content

Sampling Distributions — AP Statistics

AP Stats Guy13 min

concept

Central Limit Theorem

Khan Academy AP Stats10 min

clarification

Standard Error vs. Standard Deviation

Starnes AP Stats8 min

🎯

UNIT 712-15%

Inference: Confidence Intervals

Expand ›

Key Topics

Confidence interval structure: statistic ± critical value × SE
One-sample z-interval for proportion; one-sample t-interval for mean
Two-sample intervals: comparing two groups
Interpreting: 'We are 95% confident that the true [parameter] is between...'
Conditions: Random, Normal/Large Sample, Independence (10% condition)

Key Terms

confidence interval

range of plausible values for a population parameter

confidence level

probability that the interval captures the true parameter in repeated sampling

margin of error

critical value × standard error

critical value

z* or t* corresponding to desired confidence level

t-distribution

used when σ is unknown; heavier tails than Normal

degrees of freedom

df = n - 1 for one-sample t; determines t* value

Practice Prompt

A random sample of 50 students showed that 34 have a smartphone. (a) Check all conditions for a one-proportion z-interval. (b) Calculate a 95% confidence interval for the true proportion of students with smartphones. (c) Interpret the interval in context. (d) A school administrator says '95% of students have smartphones.' Is this consistent with your interval? Explain. (e) What sample size would you need to cut the margin of error in half?

Practice with Prof. Nadia →

Curated Video Lessons

content

Confidence Intervals — AP Statistics

AP Stats Guy14 min

content

One-Sample t-Interval

Khan Academy AP Stats11 min

critical

Conditions for Inference

Starnes AP Stats10 min

🧪

UNIT 815-18%

Inference: Significance Tests

Expand ›

Key Topics

Four-step hypothesis test: Hypotheses → Conditions → Calculations → Conclusion (HCCC)
One-sample z-test for proportion; one-sample t-test for mean
Two-sample tests; chi-square goodness of fit and test of independence
Slope of regression line: t-test for β
P-value interpretation; Type I and Type II errors; power of a test

Key Terms

null hypothesis H₀

the default assumption — no effect, no difference

alternative hypothesis Hₐ

the claim being tested — what we're looking for evidence of

p-value

probability of getting results as extreme as observed, assuming H₀ is true

Type I error

rejecting H₀ when it is actually true (false positive)

Type II error

failing to reject H₀ when it is actually false (false negative)

power

probability of correctly rejecting a false H₀ (1 - P(Type II error))

Practice Prompt

A company claims that 40% of customers prefer their new product. A random sample of 200 customers shows 92 prefer it. (a) State the null and alternative hypotheses. (b) Check all conditions for a one-proportion z-test. (c) Calculate the test statistic and p-value. (d) Using α = 0.05, state your conclusion in context. (e) What type of error could you have made? Describe what it would mean in context.

Practice with Prof. Nadia →

Curated Video Lessons

content

Hypothesis Tests — AP Statistics Complete Guide

AP Stats Guy16 min

concept

P-Values and Conclusions

Khan Academy AP Stats12 min

advanced

Chi-Square Tests — AP Statistics

Starnes AP Stats13 min

Honors Assessment

Three Assessment Types

Honors Statistics assessments reward statistical communication — defining parameters, checking conditions, and writing conclusions in context — not just correct calculations.

Get Help →

🔬

Statistical Investigation

Design a study or experiment, collect or analyze data, and present findings with statistical reasoning and appropriate displays.

Scoring Criteria

Research question is clearly defined and answerable with data

Appropriate sampling or experimental design selected and justified

Data summaries include context (variable name, units, population)

Conclusion addresses the original question with statistical evidence

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Data Analysis Report

Analyze a provided dataset using exploratory techniques, probability, or inference — and communicate findings in written form.

Scoring Criteria

Distributions described using SOCS framework with context

Graphical displays are accurate, labeled, and support the narrative

Statistical measures computed correctly with interpretation in context

Comparison language used when analyzing two or more groups

🎯

Inference Justification

Conduct a full confidence interval or significance test using the four-step HCCC framework, with complete written justification.

Scoring Criteria

Parameter defined in words before any calculation begins

All conditions checked explicitly with justification for each

Correct procedure identified, formula shown, calculation accurate

Conclusion written in context with direction of claim and significance level

Curated for Mastery

Practice & Reference Resources

🏛

OFFICIALFREE

CollegeBoard AP Statistics

Official CED, sample FRQs, and scoring guidelines.

Open resource

📂

OFFICIALFREE

Past AP Statistics FRQs (1997–2024)

Every past FRQ and scoring rubric. Practice Part A in 13-minute blocks, Part B in 25 minutes.

Open resource

🎥

HIGHLY RECOMMENDEDFREE

AP Stats Guy (Josh Tabor)

Co-author of the Starnes/Tabor textbook. Excellent video explanations of every topic and FRQ strategy.

Open resource

🎯

FREE PRACTICEFREE

Khan Academy AP Statistics

Full AP Statistics course with practice problems organized by unit. Great for checking understanding.

Open resource

📚

COMPREHENSIVEFREE

Fiveable AP Statistics

Unit summaries, FRQ practice, and live cram sessions before the May exam.

Open resource

📖

TEXTBOOK

The Practice of Statistics (Starnes & Tabor)

The official AP Statistics textbook. Read the Technology Corners for calculator tips.

Open resource

🚀

REFERENCEFREE

Stat Trek

Quick reference for probability rules, distributions, and calculator steps. Excellent as a formula cheat sheet.

Open resource

📝

PRACTICE MCQ

Albert.io AP Statistics

AP-style multiple choice practice covering all 4 main units.

Open resource

Prof. Nadia's Playbook

Six Success Tips

💬

Context every answer: never write a bare number. 'The mean is 42 minutes' is correct. 'The mean is 42' earns no credit.

📋

Use SOCS for every distribution description — Shape, Outliers, Center, Spread — in that order, every time.

✅

Check conditions explicitly before every inference procedure. Random? Normal? Independent? Write them out.

🔤

Define your parameter in words before stating hypotheses. 'Let p = the true proportion of all seniors who…'

📈

Sketch the Normal curve when solving probability problems — it helps you verify whether your answer is reasonable.

🔍

Review every missed problem by asking two questions: Was my error conceptual or procedural? What's the correct reasoning?

AI-Powered Progress

16-Week Honors Study Plan

Weeks 1–4

Phase 1: Exploring Data and Collecting Data

Master SOCS framework until it becomes automatic for every distribution description
Practice drawing and interpreting boxplots, histograms, scatterplots daily
Study design: practice identifying confounding variables in 5 studies per week
Written analysis: 2 data description write-ups per week — check for context in every sentence

Weeks 5–8

Phase 2: Probability and Sampling Distributions

Master binomial and geometric distribution formulas cold
Practice sampling distribution problems with Central Limit Theorem applications
Two probability analysis problems per week with full work shown
Calculator drills: normalcdf, invNorm, binomcdf, binompdf — master each

Weeks 9–12

Phase 3: Inference — Confidence Intervals and Tests

Complete all inference types: z-test, t-test, chi-square, regression slope
Master the four-step HCCC format until it becomes automatic
One complete inference problem per day — check conditions every time
Peer review sessions: swap written justifications and evaluate each other's reasoning

Weeks 13–16

Phase 4: Statistical Investigation and Portfolio

Design and complete a full Statistical Investigation project from question to conclusion
Compile a Data Analysis Portfolio — one polished report per unit
Review every missed problem — identify if the error is conceptual or procedural
Final sessions with Prof. Nadia (SofAI): oral explanation of your reasoning — the highest form of understanding

Agentic AI Tutoring

Your Honors Statistics AI Tutor

Prof. Nadia Osei is your Statistics expert — every data analysis, probability problem, and inference procedure. SofAIconnects Statistics to every other subject you're studying.

🎯 Walk me through the four-step inference framework with a real example 📋 I always forget to check conditions — help me master them for every test type 📊 Give me a data analysis practice problem and guide me through SOCS ⚖️ What is the difference between a confidence interval and a p-value?

📊

Ready to Master Honors Statistics?

Enroll in the most comprehensive, AI-powered Honors Statistics course available. WASC accredited. UC A-G Section C approved. Honors credit.

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WASC Accredited · UC A-G Approved · Honors Course · UC A-G Section C

Statistics / Honors Data Analysis
Think With Data

Data, Inference, Decisions

Four Mastery Areas

Honors Statistics develops four interconnected skill sets that form the foundation of data science, research, and quantitative reasoning at the college level.

🧠

Statistical Thinking

Frame questions statistically, distinguish causation from association, and recognize when data supports a claim.

📉

Data Visualization

Create and interpret histograms, boxplots, scatterplots, and two-way tables to reveal patterns in data.

🎲

Probability Reasoning

Apply probability rules, model random phenomena with distributions, and use the Normal curve fluently.

🔬

Inference Skills

Construct confidence intervals, conduct significance tests, and communicate conclusions in context with evidence.

Statistics / Honors Data AnalysisThink With Data

Four Course Pillars

Exploratory Data Analysis

Probability & Distributions

Statistical Inference

Regression & Association

Four Mastery Areas

Honors Course Goals

Eight Statistics Units

Exploring One-Variable Data

Key Topics

Key Terms

Curated Video Lessons

Exploring Two-Variable Data

Key Topics

Key Terms

Curated Video Lessons

Collecting Data

Key Topics

Key Terms

Curated Video Lessons

Probability

Key Topics

Key Terms

Curated Video Lessons

Random Variables and Probability Distributions

Key Topics

Key Terms

Curated Video Lessons

Sampling Distributions

Key Topics

Key Terms

Curated Video Lessons

Inference: Confidence Intervals

Key Topics

Key Terms

Curated Video Lessons

Inference: Significance Tests

Key Topics

Key Terms

Curated Video Lessons

Three Assessment Types

Statistical Investigation

Data Analysis Report

Inference Justification

Practice & Reference Resources

CollegeBoard AP Statistics

Past AP Statistics FRQs (1997–2024)

AP Stats Guy (Josh Tabor)

Khan Academy AP Statistics

Fiveable AP Statistics

The Practice of Statistics (Starnes & Tabor)

Stat Trek

Albert.io AP Statistics

Six Success Tips

16-Week Honors Study Plan

Phase 1: Exploring Data and Collecting Data

Phase 2: Probability and Sampling Distributions

Phase 3: Inference — Confidence Intervals and Tests

Phase 4: Statistical Investigation and Portfolio

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AP Seminar

Your Honors Statistics AI Tutor

Ready to Master Honors Statistics?

Statistics / Honors Data AnalysisThink With Data

Four Course Pillars

Exploratory Data Analysis

Probability & Distributions

Statistical Inference

Regression & Association

Four Mastery Areas

Honors Course Goals

Eight Statistics Units

Exploring One-Variable Data

Key Topics

Key Terms

Curated Video Lessons

Exploring Two-Variable Data

Statistics / Honors Data Analysis
Think With Data

Statistics / Honors Data Analysis
Think With Data