STAT 1350, 6/15 Discussion Questions

1. / A company database contains the following information about each employee: age, date hired, sex (male or female), ethnic group (Asian, black, Hispanic, etc.), job category (clerical, management, technical, etc.), and yearly salary. Which of the variables are categorical?
2. / Is a person’s test score on the SAT a good predictor of that person’s future college grade point average (GPA)? A researcher gathers data on the SAT score and college GPA for 569 college seniors. These measurements are examples of quantitative or categorical data?
3. / You have data on returns on common stocks for all years since 1945. To show clearly how returns have changed over time, what is your best choice of graph?
4. / A bar graph compares the size of the armed forces for China, North Korea, Russia, and the United States. To make the graph look nicer, the artist replaces each bar by a proportionallycorrect picture of a soldier that is enlarged or reduced to be as tall as the bar. Why is this graph considered misleading?
5. / Describe seasonal variation, and give three examples of it.

Does using a cell phone while driving make an accident more likely? Researchers compared telephone company and police records to find 699 people who had cell phones and were also involved in an auto accident. Using billing records, they compared cell phone use in the period of the accident with cell phone use the same period on a previous day. Result: The risk of an accident was four times higher when using a cell phone.

6. / The researchers also recorded the manufacturer of each subject's cell phone (Apple, Samsung, etc.). This variable is categorical or quantitative?
7. / The proper graph for showing the distribution of phones by manufacturer (i.e., number of people who own an Apple phone, number of people who own a Samsung phone, etc.) is what kind of graph? Why?
8. / When pictures replace the bars in a bar graph, the resulting graph is called what?
9. / The proper graph for showing the percentage of students in a monogamous relationship, grouped by year in school (freshman, sophomore, etc.) is what?
10. / In order to create a good graph, what are three things you should do?
11. / What tells us what values a variable takes and how often it takes those values?
12. / What does “seasonal adjustment” mean?

13. Below are a series of graphs, explain why they are good or bad graphs.

14. For each of the graphs below, describe what kind of graph it is and what kind of data (categorical or quantitative) it is displaying. Label all key features of the graph. What are the steps necessary to create each type of graph?

15. / Here is a set of data: 1300, 18, 25, 19, –7, 24. Which observation is the outlier?
16. / To display the number of pets owned by each of the 37 students in a class, what would be a good choice of graph?
17. / You want to make a graph that shows how the cost of attending your school has increased since 1980. What would be a good choice of graph?

Below is a histogram of the ages of the professors at a large university.

18. / The overall shape of this distribution is generally symmetric, skewed right or skewed left?
19. / Approximately what percentage of the professors are 30–39 years old?
20. / There are 800 professors at this university. How many of them are in their 70s?

The heights (inches) of students in a graduate-level statistics are displayed below:

Student / Bob / Sue / Pam / Lee / Mary / Carl / Ace / Moe / Ann
Height / 68 / 69 / 63 / 73 / 67 / 66 / 69 / 70 / 71
21. / What is the median height (inches) of these students? Find it by hand and then verify it in your calculator.
22. / What is the third quartile of these heights (inches)? Find it by hand and then verify it in your calculator.
23. / What is the mean of these heights (inches)? Find it by hand and then verify it in your calculator.
24. / What is the standard deviation of these heights (inches)? Find it by hand and then verify it in your calculator.
25. / What is the main advantage of boxplots (or box-and-whisper plots) over stemplots (or stem-and-leaf plots) and histograms?
26. / The calorie counts for the 17 poultry brands are:
129 132 102 106 94 102 87 99 170 113 135 142 86 143 152 146 144
What is the first quartile of the 17 poultry hot dog calorie counts?

Here are the number of hours that each of a group of students studied for an exam:

2 4 22 2 1 4 1 5 5 4

27. / What is the median number of study hours?
28. / What is the mean number of study hours?
29. / What is the third quartile of the number of study hours?
30. / What is the standard deviation of the number of study hours?
31. / The data contains one high outlier (22 hours). Which of your results for the previous four questions would change if this were 5 hours instead of 22 hours? (You do not need to calculate new values.)
32. / For a distribution that is skewed to the left, usually the
33. / The five numbers in the five-number summary are

The following is a stemplot of 12 exam scores.

(The stem is the tens place and the leaf is the ones place.):

6 8

7 66

8 0488

9 22666

34. / What is the median? [Hint: What is the list of raw data based on the chart?]
35. / What is the mean?
36. / The standard deviation is a measure of what property of a distribution?

This boxplot shows the distribution of heights of 16 undergraduate statistics students.

37. / From the above boxplot, approximately how many students are 69 inches or taller? [Hint: What is the 5 number summary, and which of those numbers is 69 inches? What does that number mean?]
38. / From the above boxplot, what height would a student have to be in order to be taller than 60% of other students?[Hint: Estimate this: 62.5% is halfway between which two numbers of the 5-number summary?]
39. / A set of measurements has this boxplot:

Which point on this boxplot is the median of the distribution? Label all key features of this graph. Does the data appear to be symmetric, skewed left or skewed right?
40. / What are two important properties of the standard deviation?
  1. What is another name for the normal distribution?
  1. Describe some important features about normal distributions.
  1. Give at least three examples of random variables that are distributed normally.
  1. What is the standard deviation of the standard normal distribution?
  1. What is the 68-95-99.7% rule? [This rule is also known as the Empirical Rule.]
  1. Fill in the picture of the standard normal distribution below and label at least 6 key features on the graph.
  1. The 68-95-99.7 Rule can also be broken down as shown on the graph below.

If the mean of a distribution is 100, and the standard deviation is 15, what percent of the population is between 70 and 115? Draw the normal distribution below and use the data from the graph above to calculate the percentage. Label all key features.

  1. Based on the graph below, what is the mean height of men? What is the mean height of women? Which group has a larger standard deviation?
  1. Use the table in your book to estimate the probability (area) under the normal distribution curve for the z-scores shown on the graph below.
  1. Suppose that the mean IQ of a certain high school is 109, with a standard deviation of 13. What is the standard score (z-score) of a student with an IQ score of 125?
  1. What is the probability that a student in the school (in #10) will have an IQ below 125?
  1. What is the probability that a student in the school (in #10) will have an IQ above 125?
  1. What is the percentile ranking represented by an IQ of 125?