AP Statistics AP Statistics
Overview and Basic Vocabulary
Key Ideas

The Meaning of Statistics

Quantitative vs. Qualitative Data

Descriptive vs. Inferential Statistics

Collecting Data

Experiments vs. Observational Studies

Random Variables
The Meaning of Statistics

Statistics is the science of data analysis.

Statistics has been developing as a field of study since
the 16th century.

Statistics is one of the most practical subjects studied in
school.

The AP Statistics exam was first offered in 1997 and
was given to 7,667 students.

By 2008, the number of students taking the exam had
increased to 108,284.

The mean score in 2008 was 2.86. 59.3% of students
scored 3 or higher.
Quantitative vs.
Qualitative

Quantitative data is also known as numerical data
and is measured or identified on a numerical scale.

Qualitative or categorical data can be classified into a
group.

Examples of quantitative data include: heights of
students in a class, GPA of a group of students,
MPG for a model of car, daily amount of rainfall in
Acworth.

Examples of qualitative data would be gender,
political affiliation, ethnicity, class (senior, junior,
etc.)
Discrete and Continuous
Data

Quantitative data can be either discrete or
continuous.

Discrete data are data that can be listed or placed in
order. Usually, but not always, there is a finite
quantity of discrete data, i.e. the list of outcomes
when rolling a single die.

Continuous data can be measured, or take on values
in an interval.

The number of heads we get on 20 flips of a coin is
discrete; the time of day is continuous.
Descriptive Statistics

Statistics has two primary functions: to describe data
and to make inferences from data.

Descriptive statistics is often referred to as exploratory
data analysis (EDA).

The components of EDA are analytical and graphical.

For one variable data, we could look at measure of
center and spread. We could graph the data to look for
shape and patterns.

For two variable data, we would look for relationships
between the variables.
Inferential Statistics

Inferential statistics involve using data from samples
to make inferences about the population from which
the sample was drawn.

We use samples to estimate some characteristic of a
population (such as average height) because it is
often too expensive or too difficult to do a census of
the entire population.
Parameters vs. Statistics

Values that describe a sample are called statistics, and
values that describe a population are called
parameters.

In inferential statistics, we use statistics to estimate
parameters.
Collecting Data

An important question in AP Statistics is how the
data are collected.

Three ways of collecting data are surveys,
experiments and observational studies.

It is extremely important to understand that data
must be gathered correctly in order to have analysis
and inference be meaningful.
Surveys

In a well-designed survey, you take a random sample
of the population of interest, compute statistics of
interest (like the proportion of high school students
who regularly wear a seatbelt), and use those to make
a prediction.

One area of concern is that subjects may not be
Experiments/
Observational Studies

Used to study the reactions of persons or things to
certain stimuli.

Both basically involve collecting comparative data on
groups (called treatment and control).

The groups are constructed so that hopefully the only
difference between them is the focus of the study.

Our goal is to generalize our findings to the
population. Our ability to do so involves the degree
to which we are convinced that the only difference
between the groups is the variable we are studying.
Random Variables

A random variable can be thought of as a numerical
outcome of a random phenomenon or experiment.

For example, if we toss three coins, and let X be the
count of heads. X can take on the values of 0, 1, 2,
or 3. This is a discrete random variable.

An example of a continuous random variable might
be the number of centimeters a child grows from age
5 to age 6.

There are a number of terms and definitions in AP
Statistics.

You may not be asked specific definitions on the
exam, but you are expected to have the working
vocabulary needed to understand any questions you