Introductory Statistics

What you will learn

• Summarize data with graphs and measures of center and spread.
• Distinguish a population from a sample.
• Use basic probability to describe uncertain outcomes.
• Interpret confidence intervals and hypothesis tests in context.
• Evaluate study design, association, and possible sources of bias.

Common challenges

• Words carry precise meanings

  Terms such as significant and random have technical meanings. Write a plain-language interpretation beside each new definition.

• College work requires more than calculation

  Compared with many high school math classes, the reading and written explanations may feel heavier. Schedule time to interpret results, not just enter numbers.

• Choosing an appropriate method

  Identify the question, variable types, and study design first. Then check the method's conditions before using software.

• Probability can feel unintuitive

  Use small tables, tree diagrams, or repeated simulations. Separate what is possible from what is likely.

Key concepts

Population and sample

A population is the full group a question concerns; a sample is the part observed. How the sample was selected affects what conclusions are justified.

Center and spread

Center describes a typical value, while spread describes variation. Always look at the distribution's shape and unusual values too.

Probability

Probability describes how likely an event is within a model. Its value ranges from 0 to 1.

Sampling variability

Different random samples usually give different statistics. Inference uses this variation to describe uncertainty.

Statistical inference

Inference uses sample data to reason about a population. Confidence intervals estimate parameters, while hypothesis tests assess evidence against a stated null model.

Association and causation

Two variables can be related without one causing the other. Random assignment in a well-designed experiment helps support causal conclusions.

How to prepare

• Review fractions, percentages, square roots, and basic equations.
• Read a graph and describe its axes, units, and overall pattern.
• Practice entering a small data set into a spreadsheet or the assigned calculator.
• Take a short study summary and identify who was observed and what was measured.

Study habits that help

• Write a conclusion in words after each calculation.
• Make a method checklist based on variable type, question, and conditions.
• Sketch the distribution before choosing summaries.
• Keep random sampling and random assignment in separate columns with examples.

What to expect

Typical workload

Moderate

Time outside class

Typically about 6–9 hours outside class weekly for a three-credit course; college, instructor, and software tasks can change the time needed. A general college rule of thumb is about 2–3 study hours outside class for each hour in class.

Pace

Early work on data and probability builds toward inference, often with regular software assignments.

How it is usually graded

Courses typically combine exams, quizzes, homework, data analyses, and sometimes a project with written interpretations.

Skills that help

• Quantitative reasoning
• Graph reading
• Careful interpretation
• Basic technology use

What teachers usually expect

• Explain answers using the study's context and units.
• Check assumptions and conditions before applying a method.
• Distinguish what the data show from what the study design allows you to conclude.

Before you start

• Colleges commonly expect algebra readiness through placement or an earlier math course; many introductory versions do not require calculus.
• Prerequisites differ by college and by the statistics course intended for your major, so check the college catalog.

These are general descriptions of a typical course. Workload, pace and prerequisites differ by school and instructor, so check with your counselor, advisor or the course catalog.

How it connects to majors

• Psychology
• Public health
• Business analytics
• Sociology
• Data science

Flashcards

Practice questions

Vocabulary

Population

The entire group a statistical question concerns.

Sample

The observed subset of a population.

Parameter

A number describing a population.

Statistic

A number calculated from sample data.

Bias

A systematic tendency for a method to favor some results over others.

Correlation

A measure of the direction and strength of a linear relationship between two quantitative variables.

Confidence interval

A range estimated from data using a method with a stated long-run coverage rate.

Null hypothesis

A specific claim about a population used as the starting model for a hypothesis test.