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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 honest in answering your questions. 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. Note about Vocabulary 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 may be asked. Bottom line? KNOW YOUR VOCABULARY! Assignment Read Chapter P in your textbook – pages 5 – 33. Problems: starting on page 11, P.1 – P.28