Describing Data: Graphs and Tables s1
CHAPTER 1
DESCRIBING DATA: GRAPHS AND TABLES
MULTIPLE CHOICE QUESTIONS
In the following multiple-choice questions, please circle the correct answer.
1. Data that arise from counts are called:
a. continuous
b. nominal
c. counted
d. discrete
ANSWER: d
2. A sample of a population taken at one particular point in time is categorized as:
a. categorical
b. discrete
c. cross-sectional
d. time-series
ANSWER: c
3. Gender and State are examples of which type of data?
a. Discrete
b. Continuous
c. Categorical
d. Ordinal
ANSWER: c
4. A histogram that is positively skewed is:
a. skewed to the right
b. skewed to the left
c. balanced
d. symmetric
ANSWER: a
5. A histogram that has exactly two peaks is called a distribution.
a. unimodal
b. bimodal
c. skewed
d. scatter
ANSWER: b
6. An opinion variable expressed numerically on a 1-5 scale is a(n):
a. histogram
b. opinion poll
c. categorical scale
d. Likert scale
ANSWER: d
7. A variable is classified as ordinal if:
a. there is a natural ordering of categories
b. there is no natural ordering of categories
c. the data arises from continuous measurements
d. we track the variable through a period of time
ANSWER: a
8. A population includes:
a. only people
b. only households
c. all objects of interest in a particular study
d. only machines
ANSWER: c
9. Researchers try to gain insight into the characteristics of a population by examining a ______of the population.
a. model
b. sample
c. description
d. replica
ANSWER: b
10. Numerical variables can be subdivided into which two types?
a. Diverse and categorical
b. Discrete and continuous
c. Nominal and progressive
d. Cross-sectional and discrete
ANSWER: b
11. The tool that provides useful information about a data set by breaking it down into subpopulations is:
a. the histogram
b. the scatterplot
c. the pivot table
d. the spreadsheet
ANSWER: c
12. The tables that result from pivot tables are called:
a. samples
b. sub-tables
c. specimens
d. crosstabs
ANSWER: d
13. In order for the characteristics of a sample to be generalized to the entire population, it should be ______of the population.
a. symbolic
b. typical
c. representative
d. illustrative
ANSWER: c
14. A bimodal histogram is often an indication that:
a. the data are incorrect
b. the data are inconclusive
c. the sample is not representative of the population
d. the data come from two or more distinct populations
ANSWER: d
15. The Literary Digest fiasco of 1936 is an example of:
a. a sample that is not representative of its population
b. an incomplete population
c. an inconclusive data set
d. a symmetric histogram
ANSWER: a
16. A ______indicates how many observations fall into various categories.
a. Likert scale
b. frequency table
c. sample table
d. tabulation scale
ANSWER: b
17. A ______is the graphical analog of a frequency table.
a. histogram
b. graph
c. diagram
d. table
ANSWER: a
18. A histogram that has a single peak and looks approximately the same to the left and right of the peak is:
a. bimodal
b. symmetric
c. balanced
d. proportional
ANSWER: b
19. An observation is a:
a. variable
b. field
c. member of a population or sample
d. characteristic of a population
ANSWER: c
20. If data is stored in a database package, which of the following terms are typically used?
a. Fields and records
b. Cases and columns
c. Variables and samples
d. Variables and observations
ANSWER: a
21. A scatterplot allows one to see:
a. whether there is any relationship between two variables
b. what type of relationship there is between two variables
c. both a and b
d. neither a nor b
ANSWER: c
22. A time series plot is essentially a:
a. histogram
b. scatterplot
c. diagram
d. figure
ANSWER: b
23. The commonly observed shapes of histograms are:
I. symmetric II. asymmetric III. bimodal
IV. polymodal V. positively skewed VI. negatively skewed
a. I, II, III and IV
b. III, IV, V, and VI
c. II, III, IV, and V
d. I, III, V, and VI
ANSWER: d
24. When we look at a time series plot, we usually look for which two things?
a. “Is there an observable trend?” and “Is there a seasonal pattern?”
b. “Is there an observable trend” and “Can we make predictions?”
c. “Is the sample representative?” and “Is there a seasonal pattern?”
d. “Is there an observable trend?” and “Is the trend symmetric?”
ANSWER: a
TEST QUESTIONS
25. The students at small community college in Iowa apply to study either English or business. Some administrators at the college are concerned that women are being discriminated against in being allowed admittance, particularly in the business program. Below, you will find two pivot tables that show the percentage of students admitted by gender to the English program and the business school. The data has also been presented graphically. What do the data and graphs indicate?
English program
Gender / No / Yes / TotalFemale / 46.0% / 54.0% / 100%
Male / 60.8% / 39.2% / 100%
Total / 53.5% / 46.5% / 100%
Business school
Gender / No / Yes / TotalFemale / 69.2% / 30.8% / 100%
Male / 64.1% / 35.9% / 100%
Total / 65.4% / 34.6% / 100%
ANSWER:
These data indicate that a smaller percentage of women are being admitted to the business program. Only 30.8% of women are being admitted to the business program compared to 35.9% for men. However, it is also important to note that only 34.6% of all applicants (women and men) are admitted to the business program compared to 46.5% for the English program. Maybe the males should say something about being discriminated against in being admitted to the English program.
26. A sample of 30 schools produced the pivot table shown below for the average percentage of students graduating from high school. Use this table to determine how the type of school (public or Catholic) that students attend affects their chance of graduating from high school.
ANSWER:
The percentages in the right column suggest that if we look at all schools, the rate of graduation is much higher in Catholic schools than in public schools. But a look at the breakdowns in the three ethnic group columns shows that this difference is due primarily to schools that are black and Latino. There isn't much difference in graduation rates between Catholic and public schools that are white.
27. The data below represents monthly sales for two years of beanbag animals at a local retail store (Month 1 represents January and Month 12 represents December). Given the time series plot below, do you see any obvious patterns in the data? Explain.
ANSWER:
This is a representation of seasonal data. There seems to be a small increase in months 3, 4, and 5 and a large increase at the end of the year. The sales of this item seem to peak in December and have a significant drop off in January.
28. A data set from a sample of 399 Michigan families was collected. The characteristics of the data include family size (large or small), number of cars owned by family (1, 2, 3, or 4), and whether family owns a foreign car. Excel produced the pivot table shown below.
Use this pivot table to determine how family size and number of cars owned influence the likelihood that a family owns a foreign car.
ANSWER:
The pivot table shows that the more cars a family owns, the more likely it is that they own a foreign car (makes sense!). Also, the percentage of large families who own a foreign car is larger than the similar percentage of small families (36.0% versus 10.4%).
29. An operations management professor is interested in how her students performed on her midterm exam. The data and histogram are presented below. The histogram represents the distribution of exam scores (where the maximum score is 100) for 50 students.
Student / Score / Student / Score / Student / Score / Student / Score1 / 72 / 14 / 78 / 27 / 83 / 40 / 84
2 / 95 / 15 / 72 / 28 / 87 / 41 / 78
3 / 83 / 16 / 73 / 29 / 82 / 42 / 84
4 / 85 / 17 / 75 / 30 / 72 / 43 / 71
5 / 65 / 18 / 79 / 31 / 97 / 44 / 77
6 / 82 / 19 / 80 / 32 / 88 / 45 / 78
7 / 84 / 20 / 87 / 33 / 70 / 46 / 70
8 / 74 / 21 / 80 / 34 / 83 / 47 / 86
9 / 74 / 22 / 91 / 35 / 92 / 48 / 67
10 / 82 / 23 / 74 / 36 / 94 / 49 / 91
11 / 81 / 24 / 69 / 37 / 63 / 50 / 78
12 / 75 / 25 / 88 / 38 / 83
13 / 78 / 26 / 84 / 39 / 81
Based on this histogram, how would you characterize the students’ performance on this exam?
ANSWER:
Exam scores are fairly normally distributed. Majority of scores (76%) are between 70 and 90 points, while 12% of scores are above 90 and 12% of scores are 70 or below.
30. A health magazine reported that a man’s weight at birth has a significant impact on the chance that the man will suffer a heart attack during his life. A statistician analyzed a data set for a sample of 798 men, and produced the pivot table and histogram shown below. Determine how birth weight influences the chances that a man will have a heart attack.
ANSWER:
The above pivot table shows counts (as percentages of row) of heart attack versus birth weight, where birth weight has been grouped into categories. The percentages in each category with heart attacks have then been plotted versus weight at birth as shown in the histogram. It appears that the likelihood of a heart attack is greatest for light babies, and then decreases steadily, but increases slightly for the heaviest babies.
31. The table shown below contains information technology (IT) investment as a percentage of total investment for eight countries during the 1990s. It also contains the average annual percentage change in employment during the 1990s. Explain how these data shed light on the question of whether IT investment creates or costs jobs.
Country / % IT / % ChangeNetherlands / 2.5% / 1.6%
Italy / 4.1% / 2.2%
Germany / 4.5% / 2.0%
France / 5.5% / 1.8%
Canada / 8.3% / 2.7%
Japan / 8.3% / 2.7%
Britain / 8.3% / 3.3%
U.S. / 12.4% / 3.7%
for eight countries during the 1990s
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15
15
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ANSWER:
QUESTIONS 32 THROUGH 35 ARE BASED ON THE FOLLOWING INFORMATION:
A real estate agent has gathered information on 40 houses that were recently sold in a local community. The data below represents the following variables: the selling price of each house (in thousands of dollars), the appraised value of each house (in thousands of dollars), the size of the house (in hundreds of square feet), and the number of bedrooms.
House / Value / Price / Sq. Footage / # of Bedrooms1 / 121.87 / 119.37 / 20.5 / 4
2 / 122.78 / 130.39 / 15.9 / 3
3 / 144.35 / 135.70 / 18.6 / 3
4 / 116.20 / 126.30 / 12.1 / 2
5 / 139.49 / 137.08 / 17.1 / 3
6 / 144.80 / 139.53 / 17.2 / 3
7 / 107.06 / 114.34 / 16.7 / 3
8 / 147.47 / 140.04 / 16.5 / 3
9 / 135.12 / 136.01 / 16.1 / 2
10 / 140.24 / 140.93 / 15.7 / 3
11 / 129.89 / 132.42 / 16.5 / 4
12 / 121.14 / 118.30 / 16.4 / 3
13 / 157.79 / 155.55 / 22.7 / 5
14 / 135.57 / 128.50 / 19.7 / 4
15 / 151.99 / 143.36 / 18.2 / 3
16 / 120.53 / 119.65 / 16.5 / 3
17 / 118.64 / 122.57 / 14.7 / 2
18 / 149.51 / 145.27 / 18.5 / 4
19 / 146.86 / 149.73 / 21.7 / 4
20 / 152.84 / 156.13 / 19.6 / 3
21 / 122.27 / 126.72 / 19.2 / 4
22 / 145.71 / 141.13 / 18.5 / 3
23 / 138.38 / 136.53 / 14.3 / 2
24 / 109.46 / 118.04 / 13.9 / 2
25 / 144.68 / 153.70 / 21.3 / 4
26 / 133.27 / 126.31 / 18.9 / 4
27 / 133.27 / 134.02 / 16.4 / 2
28 / 150.38 / 141.56 / 20.7 / 3
29 / 135.26 / 142.96 / 18.1 / 3
30 / 112.60 / 118.53 / 14.6 / 2
31 / 114.23 / 121.59 / 14.1 / 2
32 / 153.24 / 146.40 / 21.9 / 4
33 / 125.89 / 141.25 / 15.8 / 3
34 / 135.62 / 130.73 / 18.4 / 3
35 / 121.45 / 115.97 / 16.3 / 2
36 / 132.45 / 125.21 / 15.8 / 3
37 / 135.83 / 130.37 / 17.6 / 3
38 / 125.76 / 119.75 / 18.1 / 4
39 / 125.84 / 120.93 / 17.1 / 3
40 / 135.32 / 126.80 / 18.9 / 3
32. Indicate whether each of the four variables is continuous or discrete.