Clotilde Ifrán

1. The word statisticshas four distinct meanings. List them.

2. The chapter mentions several benefits of studying statistics. List at least three benefits.

3. How does the original meaning of the term populationdiffer from today’s sta- tistical definition?

4. For each of the following statements, indicate (a) the population, (b) the ele- ment, and (c) the observation to be recorded.

a. In the previous presidential election, 36% of 18- to 24-year-olds voted. b. Approximately 16% of all children under 18 are members of families whose

incomes are below the poverty level.

c. Approximately 42% of all prison inmates are 21 to 26 years old.

d. Approximately 32% of all high school graduates 18 to 24 years old are en- rolled in college.

e. Four out of 10 Americans are under 25 years old.

f. According to a recent Centers for Disease Control report, one of every 1,667 American white women between the ages of 27 and 39 has the AIDS virus. g. According to the U.S. Department of Education, 38.4% of male high

school students have performed a community service during the past two years.

5. (a) Why is most research conducted on samples rather than populations? (b) How is sample size related to the resemblance between a random sample and the population?

6. Distinguish between descriptive and inferential statistics.

7. Mathematicians and behavioral scientists have somewhat different interests in numbers. Discuss these differences.

8. Ignoring for the moment the limitations of measuring instruments, classify measures of the following variables according to the mathematician’s scheme (unordered qualitative, U; ordered qualitative, O; discrete quantitative, D; continuous quantitative, C).

a. Employee production on an assembly line b. Paper-and-pencil test of creativity c. Political party affiliation

d. Final standing of football teams in the Big 12 Conference e. Weight loss after jogging 3 miles

f. Number of reported suicides in 2003 g. Major in college

h. Religious preference

i. Grading scale in school (A, B, C, D, F) j. Amount of rainfall

k. Sexual orientation (heterosexual, lesbian, gay man, bisexual woman or man) 9. Because of the limitations of measuring instruments, the measurement of some variables is of necessity approximate. Classify the variables in Exercise 8 ac- cording to whether our measurement is exact (E) or approximate (A).

10. Reclassify the variables in Exercise 8 according to the mathematician’s scheme, taking into account limitations in our ability to measure some of the variables.

11. (a) In what three ways do behavioral scientists use numbers in measurement? (b) Give three examples of each use.

12. Classify the variables in Exercise 8 with respect to level of measurement, taking into account limitations in our ability to measure some of the variables.

13. For each level of measurement, list the properties that characterize the numbers assigned to the equivalence classes.

14. Who is in the best position to determine the degree of correspondence between a set of numbers and the corresponding equivalence classes and hence to deter- mine the arithmetic operations that can meaningfully be applied?

15. What does a score of 0 on an achievement test mean?

16. Suppose that a group of inner-city students improved their arithmetic achieve- ment test scores by an average of 8 points, whereas a group of students from an affluent neighborhood improved their scores only by an average of 6 points. Explain how it is possible that the 6-point increase might actually represent a greater increase in arithmetic achievement than the 8-point increase.

1.6 Looking Back: What have you Learned?

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17. List at least one major contribution that each of the following men made to statistics.

a. Abraham de Moivre (1667–1754)

b. Lambert Adolphe Jacques Quetelet (1796–1874) c. Francis Galton (1822–1911)

d. Karl Pearson (1857–1936)

e. William Sealey Gosset (1876–1937) f. Ronald A. Fisher (1890–1962) g. Jerzy Neyman (1894–1981) h. Egon Pearson (1895–1981)

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2

Frequency

Distributions

and Graphs

Looking Ahead: What Is This Chapter About? Need to Depict and

Summarize Data 2.2 Frequency Distributions Ungrouped Frequency Distribution for Quantitative Variables Grouped Frequency Distribution for Quantitative Variables Determining the Number

and Size of Class Intervals for a Quantitative Variable The Pros and Cons of

Grouping Data Relative Frequency Distributions Cumulative Frequency Distributions Frequency Distributions for Qualitative Variables Check Your Understanding

of Section 2.2

2.3 Introduction to Graphs 2.4 Graphs for Qualitative

Variables

Bar Graph Pie Chart

Check Your Understanding of Section 2.4

2.5 Graphs for Quantitative Variables

Histogram

Frequency Polygon Cumulative Polygon Stem-and-Leaf Display Check Your Understanding

of Section 2.5 2.6 Shapes of Distributions Bell-Shaped Distributions Skewed Distributions Bimodal Distributions J,U, and Rectangular Distributions

Check Your Understanding of Section 2.6

2.7 Misleading Graphs

Check Your Understanding of Section 2.7

2.8 Looking Back: What

Have You Learned?

Review Exercises for Chapter 2

2.1 INTRODUCTION

Looking Ahead: What Is This Chapter About?

This chapter describes two kinds of procedures for depicting and summarizing data: frequency distributions and graphs. The procedures for constructing frequency distri- butions for quantitative variables differ slightly from those used to construct fre- quency distributions for qualitative variables. Also, different kinds of graphs are used to depict the two kinds of variables. The chapter ends with a description of some commonly encountered distributions and some ways that graphs can mislead you.

After reading the chapter, you should know the following:

■ How to construct frequency distributions for quantitative and qualitative variables

■ The merits of relative frequency distributions and cumulative frequency distributions

■ How to construct bar graphs and pie charts for qualitative variables

■ How to construct histograms, frequency polygons, cumulative polygons, and stem-and-leaf displays for quantitative variables

■ The names of commonly encountered distributions and four important proper- ties of distributions

■ How you can be mislead by graphs