One-Variable Data Analysis Review Problems for AP Statistics

Review the following concepts if necessary:

• Graphical Analysis for AP Statistics
• Histogram for AP Statistics
• Measures of Center for AP Statistics
• Measures of Spread for AP Statistics
• Position of a Term in a Distribution for AP Statistics
• Normal Distribution for AP Statistics

Problems

1. Which of the following are examples of quantitative data?
   1. The number of years each of your teachers has taught
   2. Classifying a statistic as quantitative or qualitative
   3. The length of time spent by the typical teenager watching television in a month
   4. The daily amount of money lost by the airlines in the 15 months after the 9/11 attacks
   5. The colors of the rainbow
2. Which of the following are discrete and which are continuous?
   1. The weights of a sample of dieters from a weight-loss program
   2. The SAT scores for students who have taken the test over the past 10 years
   3. The AP Statistics exam scores for the almost 50,000 students who took the exam in 2002
   4. The number of square miles in each of the 20 largest states
   5. The distance between any two points on the number line
3. Just exactly what is statistics and what are its two main divisions?
4. What are the main differences between the goals of a survey and an experiment?
5. Why do we need to understand the concept of a random variable in order to do inferential statistics?

Solutions

1. a, c, and d are quantitative.
2. a, d, and e are continuous; b and c are discrete. Note that (d) could be considered discrete if what we meant by "number of square miles" was the integer number of square miles.
3. Statistics is the science of data. Its two main divisions are data analysis and inference. Data analysis (EDA) utilizes graphical and analytical methods to try to see what the data "say." That is, EDA looks at data in a variety of ways in order to understand them. Inference involves using information from samples to make statements or predictions about the population from which the sample was drawn.
4. A survey, based on a sample from some population, is usually given in order to be able to make statements or predictions about the population. An experiment, on the other hand, usually has as its goal studying the differential effects of some treatment on two or more samples, which are often comprised of volunteers.
5. Statistical inference is based on being able to determine the probability of getting a particular sample statistic from a population with a hypothesized parameter. For example, we might ask how likely it is to get 55 heads on 100 flips of a fair coin. If it seems unlikely, we might reject the notion that the coin we actually flipped is fair. The probabilistic underpinnings of inference can be understood through the language of random variables. In other words, we need random variables to bridge the gap between simple data analysis and inference.