AP Stats 1.1: Introducing Statistics

What topic 1.1 covers

Topic 1.1 opens AP Statistics by defining what a statistical study is and the vocabulary you will use all year. A statistical study collects data from a sample to answer an investigative question about a larger population. You run one when the population is too large or it is too hard to collect data from every individual, so you measure a subset and reason from it. This topic sits at the front of Unit 1, the most heavily weighted unit at 20-30% of the multiple-choice section.

Population, sample, and data

A population consists of all the items or individuals of interest, and its size is written with a capital $N$. A sample is a subset of the population that you actually measure, and its size is written with a lowercase $n$. A single piece of information about one item or individual is a datum, and a collection of data is a data set.

Every number you compute traces back to a real setting. The CED calls this working "in context": a mean commute time is not just 24, it is 24 minutes for the students in your sample. Naming that context is what turns a bare number into a statistical result, and it is where students most often lose free-response points. Population and sample return in every later unit, so it is worth fixing them now, before topic 1.2 adds the matching terms for their summaries in parameter vs statistic.

Writing an investigative question

An investigative question drives the whole study, so it needs a defined purpose that you fix before the data arrive. You should not change the question after seeing the results, because that turns exploration into cherry-picking. The question must also be posed so that the data you need can actually be collected and analyzed.

For example, "What proportion of students at this school bike to class?" is answerable, because the variable is clear and you can collect it. "Is biking good?" is not, because there is no measurable variable behind it. A clear question also tells you which variable to measure and on whom, which is the bridge to the data-collection topics later in the unit. Topic 1.10 returns to this idea and breaks an investigative question into parts that guide collection, analysis, and conclusions.