Statistics is the science of learning from data in the presence of variability. A good study starts with an investigative question, collects data from a sample, and uses statistics to say something about the whole population. Sort questions, then take random samples and watch the statistic bounce around the parameter.
Statistics starts with a question that expects variability in the answers. Sort each question, then sample from a population to see why a statistic changes from sample to sample while the parameter stays fixed.
A statistical question anticipates variability: answering it needs data from many individuals (or many repeated measurements) that will not all be the same.
The population below is all 1,000 students at a school. We know the truth because this is a simulation. In real life you only see the sample.
Individuals differ, measurements differ, and samples differ. If everything were identical, one observation would tell you everything. Statistics gives tools for drawing conclusions when values vary.
A statistical question anticipates variability in the data that answer it. “How tall are 10th graders?” is statistical. “How tall is Ana?” is not.
Ask a question, collect data, analyze the data, then interpret the results in context. The interpretation often leads to a new question.
The population is the entire group of interest. A sample is the part of the population you actually collect data from.
A parameter describes a population (μ, p, σ). A statistic describes a sample (x̄, p̂, s). Memory trick: Parameter goes with Population, Statistic with Sample.
Different random samples give different statistics. That variability is predictable, which is what makes inference later in the course possible.
Identify the pieces of a study. AP questions often ask for exactly these.
| Situation | Population | Sample | Parameter | Statistic |
|---|---|---|---|---|
| A poll of 1,200 U.S. adults finds 41% approve of a new law. | All U.S. adults | The 1,200 adults polled | Proportion of all U.S. adults who approve (p) | p̂ = 0.41 |
| A factory tests 40 bulbs from today's run; mean life is 1,012 hours. | All bulbs made today | The 40 tested bulbs | Mean life of all bulbs today (μ) | x̄ = 1,012 hours |
| A teacher surveys 25 of her 150 students; 8 own a pet rabbit. | Her 150 students | The 25 surveyed | Proportion of all 150 with a rabbit | p̂ = 8/25 = 0.32 |
| The census reports the median age of all residents is 38.9 years. | All residents | None (a census) | Median age = 38.9 is a parameter | No statistic needed |
AP-style multiple choice. Pick an answer to see the explanation.
The vocabulary for topic 1.1. Read the list, flip through flashcards, or quiz yourself. For every term in the unit, see the Unit 1 terminology guide.