Deck 2: Basic Descriptive Statistics: Percentages, Ratios and Rates, Tables, Charts and Graphs

Question 1

A city of 1567 people had 34 auto thefts last year.The auto theft rate for this city

A)cannot be determined from the information given
B)is falling
C)is (34/1567)´ 100,000
D)is (100,000 ´ 1567)/34

Answer 1

is (34/1567)´ 100,000

Question 2

Twenty-three of the 50 states rejected a proposed constitutional amendment to make the house fly the National Insect.What percentage is this?

A)23%
B)25%
C)46%
D)54%

Answer 2

46%

Question 3

The sum of the proportions for all categories of a variable will be

A)100.00.
B)10.00.
C)1.00.
D)0.10.

Answer 3

1.00.

Question 4

To find the ratio of smokers to non-smokers,you would

A)divide the number of non-smokers by the number of smokers.
B)add them together and divide by the number of smokers.
C)divide the number of smokers by the number of non-smokers.
D)multiply the number of smokers by the total number of people.

Question 5

A class has 20 men and 10 women.The ratio of women to men is

A)2 to 1.
B)1 to 2.
C)20%.
D).2.

Question 6

Table 2.1
$\begin{array}{|l|l|l|}\hline \underline { \text { TABLE 2.1 POLITICAL PARTY }}\\\underline { \text { MEMBERSHIP IN TWO }}\\\underline { \text { COMMUNITIES}}\\ \hline \text { PARTY: } & \text { COMMUNITY A } & \text { COMMUNITY B } \\\hline \text { Republican } & 103 & 17 \\\hline \text { Democrat } & 135 & 21 \\\hline \text { Independent } & 17 & 15 \\\hline \text { Socialist } & \underline 9 & \underline {11} \\\hline \text { TOTALS: } & 264 & 64\\\hline\\\end{array}$
In Table 2.1,which community has the higher proportion of Independents?

A)Community A
B)Community B
C)Neither
D)This proportion can't be determined from the information given.

Question 7

Forty of every two hundred students attend all of their classes.What percentage of the student body is this?

A)5%
B)50%
C)2%
D)20%

Question 8

The homicide rate for a city is reported as 23.89.This means that

A)for every homicide,there were 23.89 victims.
B)for every 100,000 people in the population there were 23.89 homicides.
C)the homicide rate is rising.
D)there was an average of 23.89 homicides each month.

Question 9

When working with a very small number of cases,it is usually preferable to report

A)percentages.
B)proportions.
C)fractions.
D)actual frequencies.

Question 10

To be converted to a percentage,the proportion must be multiplied by

A)10.
B)100.
C)1000.
D)any of the above

Question 11

Table 2.1
$\begin{array}{|l|l|l|}\hline \underline { \text { TABLE 2.1 POLITICAL PARTY }}\\\underline { \text { MEMBERSHIP IN TWO }}\\\underline { \text { COMMUNITIES}}\\ \hline \text { PARTY: } & \text { COMMUNITY A } & \text { COMMUNITY B } \\\hline \text { Republican } & 103 & 17 \\\hline \text { Democrat } & 135 & 21 \\\hline \text { Independent } & 17 & 15 \\\hline \text { Socialist } & 9 & 11 \\\hline \text { TOTALS: } & 264 & 64\\\hline\\\end{array}$
In Table 2.1,what is the ratio of Socialists to Democrats in Community B?

A)11:21
B)11:64
C)64:11
D)9:11

Question 12

Which of the following is an impossible value for a percentage?

A)0.0%
B)47.458923%
C)110.00%
D)0.05%

Question 13

The ratio of men to women in a karate class is 3.3:1.If there are 100 women,how many men are there?

A)33
B)66
C)133
D)330

Question 14

The crude birth rate of a city that has 250 births in a year and a population of 7500 would be found by using which of the following?

A)crude birth rate = (250/7500)´ 1000
B)crude birth rate = 7500/250
C)crude birth rate = (1000/7500)´ 250
D)crude birth rate = (250/1000)´ 7500

Question 15

Table 2.1
$\begin{array}{|l|l|l|}\hline \underline { \text { TABLE 2.1 POLITICAL PARTY }}\\\underline { \text { MEMBERSHIP IN TWO }}\\\underline { \text { COMMUNITIES}}\\ \hline \text { PARTY: } & \text { COMMUNITY A } & \text { COMMUNITY B } \\\hline \text { Republican } & 103 & 17 \\\hline \text { Democrat } & 135 & 21 \\\hline \text { Independent } & 17 & 15 \\\hline \text { Socialist } & \underline 9 & \underline {11} \\\hline \text { TOTALS: } & 264 & 64\\\hline\\\end{array}$
In Table 2.1,what percentage of Democrats lives in community B?

A)(21/64)´ 100 = 32.8
B)(21/328)´ 100 = 6.4
C)(21/156)´ 100 = 13.5
D)(64/264)´ 100 = 24.2

Question 16

The purpose of univariate descriptive statistics is to

A)summarize relationships between many variables.
B)display the essential meaning of variables measured at the interval-ratio level.
C)combine nominal and discrete variables.
D)summarize a single variable.

Question 17

Table 2.1
$\begin{array}{|l|l|l|}\hline \underline { \text { TABLE 2.1 POLITICAL PARTY }}\\\underline { \text { MEMBERSHIP IN TWO }}\\\underline { \text { COMMUNITIES}}\\ \hline \text { PARTY: } & \text { COMMUNITY A } & \text { COMMUNITY B } \\\hline \text { Republican } & 103 & 17 \\\hline \text { Democrat } & 135 & 21 \\\hline \text { Independent } & 17 & 15 \\\hline \text { Socialist } & \underline 9 & \underline {11} \\\hline \text { TOTALS: } & 264 & 64\\\hline\\\end{array}$
In Table 2.1,which is the correct fraction for determining the proportion of Independents in community B?

A)15/17
B)15/264
C)64/15
D)15/64

Question 18

Table 2.1
$\begin{array}{|l|l|l|}\hline \underline { \text { TABLE 2.1 POLITICAL PARTY }}\\\underline { \text { MEMBERSHIP IN TWO }}\\\underline { \text { COMMUNITIES}}\\ \hline \text { PARTY: } & \text { COMMUNITY A } & \text { COMMUNITY B } \\\hline \text { Republican } & 103 & 17 \\\hline \text { Democrat } & 135 & 21 \\\hline \text { Independent } & 17 & 15 \\\hline \text { Socialist } & 9 & 11 \\\hline \text { TOTALS: } & 264 & 64\\\hline\\\end{array}$
In Table 2.1,what percentage of Community A are Republicans?

A)(103/264)´ 100 = 39.02
B)(103/17)´ 100 = 605.88
C)(264/328)´ 100 = 80.49
D)(103/135)´ 100 = 76.30

Question 19

Table 2.1
$\begin{array}{|l|l|l|}\hline \underline { \text { TABLE 2.1 POLITICAL PARTY }}\\\underline { \text { MEMBERSHIP IN TWO }}\\\underline { \text { COMMUNITIES}}\\ \hline \text { PARTY: } & \text { COMMUNITY A } & \text { COMMUNITY B } \\\hline \text { Republican } & 103 & 17 \\\hline \text { Democrat } & 135 & 21 \\\hline \text { Independent } & 17 & 15 \\\hline \text { Socialist } & \underline 9 & \underline {11} \\\hline \text { TOTALS: } & 264 & 64\\\hline\\\end{array}$
In Table 2.1,what is the ratio of Independents to Socialists in Community A?

A)15:11
B)17:9
C)9:17
D)17:264

Question 20

To calculate a proportion,the number of cases in any category (f)is divided by

A)the total number of categories (k).
B)the number of cases in all categories (N).
C)the cases in that category (f).
D)the number of cases in adjacent categories (k-1).

Question 21

A frequency distribution should reflect a balance of

A)detail and conciseness.
B)time and money.
C)questions and answers.
D)elegance and symmetry.

Question 22

A nation had a birth rate of 20 in 1990.The rate fell to 13 in 2000.What was the percentage change?

A)
$\left(\frac{20-13}{20}\right) \times 100=35 \%$
B)
$\left(\frac{20-13}{13}\right) \times 100=54 \%$
C)
$\left(\frac{13-20}{20}\right) \times 100=-35 \%$
D)
$\left(\frac{13-20}{13}\right) \times 100=-54 \%$

Question 23

The midpoints of intervals for frequency distributions constructed with interval-ratio variables are found by

A)adding the upper and lower class limits for each interval and then dividing by 2.
B)multiplying the upper and lower class limits for each interval.
C)dividing the range by 10.
D)None of the above.Class intervals for interval-ratio variables do not have midpoints.

Question 24

A police department reports that the number of reported rapes in their jurisdiction increased by 100% over the past decade.This means that the number of reported rapes today is

A)double the number 10 years ago.
B)actually about the same as 10 years ago.
C)equal to the number 10 years ago plus 50%.
D)triple the number 10 years ago.

Question 25

City A (population = 1567 people)had 34 auto thefts last year.City B (population = 34,567)had 40 auto thefts in the same time period and City C (population = 156,980)had 70 auto thefts.Which city had the highest RATE of auto theft?

A)City A
B)City B
C)City C
D)More information is needed to answer this question.

Question 26

Table 2.2
$\begin{array}{|l|l|l|}\hline \text {TABLE 2.2 AGES OF}\\\text {RESPONDENTS}\\\hline \text { ClassIntervals } & \text { Frequency } & \text { Percentages } \\\hline 18-23 & 5 & \\\hline 2429 & 21 & \\\hline 30-40 & 10 & \\\hline \text { TOTAL } & 36 & \\\hline\\\end{array}$
A possible problem with Table 2.2 is that

A)class intervals overlap.
B)class intervals are too large.
C)class intervals are unequal in size.
D)class intervals are exhaustive.

Question 27

Proportions and percentages,ratios and rates are all ways of expressing

A)concise distributions of a variable
B)data without leaving out any details
C)relative frequencies
D)raw frequencies

Question 28

For the following stated limits:
23-30
31-38
39-46
What are the real limits?

A)22-31
31-38
38-45

B)23-29
29-38
38-46

C)23.0-29.9
30)0-37.9
38)0-46.9

D)22.5-30.5
30)5-38.5
38)5-46.5

Question 29

As a very general rule,frequency distributions should have ____ categories.

A)less than 5
B)more than 20
C)no more than 5
D)about 10

Question 30

A small town of 1,709 residents had one homicide in the past year.The homicide rate for this town

A)cannot be determined from the information given.
B)is (1/1709)´ 100,000.
C)is rising.
D)is (1709:1)´ 1,000.

Question 31

Table 2.2
$\begin{array}{|l|l|l|}\hline \text {TABLE 2.2 AGES OF}\\\text {RESPONDENTS}\\\hline \text { ClassIntervals } & \text { Frequency } & \text { Percentages } \\\hline 18-23 & 5 & \\\hline 2429 & 21 & \\\hline 30-40 & 10 & \\\hline \text { TOTAL } & 36 & \\\hline\\\end{array}$
In Table 2.2,what is the ratio of 30-40 year olds to 18-23 year olds?

A).24
B)4.20
C)2.00
D)1.00

Question 32

Table 2.2
$\begin{array}{|l|l|l|}\hline \text {TABLE 2.2 AGES OF}\\\text {RESPONDENTS}\\\hline \text { ClassIntervals } & \text { Frequency } & \text { Percentages } \\\hline 18-23 & 5 & \\\hline 2429 & 21 & \\\hline 30-40 & 10 & \\\hline \text { TOTAL } & 36 & \\\hline\\\end{array}$
In Table 2.2,what proportion of cases are 18-23?

A)0.05
B)0.36
C)0.78
D)0.13

Question 33

Table 2.2
$\begin{array}{|l|l|l|}\hline \text {TABLE 2.2 AGES OF}\\\text {RESPONDENTS}\\\hline \text { ClassIntervals } & \text { Frequency } & \text { Percentages } \\\hline 18-23 & 5 & \\\hline 2429 & 21 & \\\hline 30-40 & 10 & \\\hline \text { TOTAL } & 36 & \\\hline\\\end{array}$
In Table 2.2,what percentage of cases is in the 18-23 age group?

A)(5/36)´ 100 = 13.51%
B)(18/23)´ 100 = 78.26%
C)(36/5)´ 100 = 7.4%
D)(5/21)´ 100 = 23.81%

Question 34

If 60 cases range in score from 4 to 84 and you want 10 intervals in a frequency distribution,approximately what will be the width of each interval?

A)4
B)8
C)12
D)60

Question 35

When constructing a frequency distribution,the number of class intervals,in general,should be

A)more than 20.
B)about 10.
C)only 2.
D)the same as the number of cases.

Question 36

Cumulative frequencies and cumulative percentages allow a researcher to

A)be sure the column totals are correct.
B)tell at a glance how many cases fall above or below a given category.
C)show the accuracy of his or her findings.
D)all of the above

Question 37

The class intervals below represent ages of respondents.Which set of intervals is both exhaustive and mutually exclusive?

A)18-19
19-20
20-21
B)18-19
20-21
22-23
C)18-20
22-24
26-28
D)18-19
21-22
24-25

Question 38

Frequency distributions may be compiled for variables measured at which level?

A)nominal
B)ordinal
C)interval-ratio
D)all of the above

Question 39

When constructing frequency distributions for variables measured at the interval-ratio level,approximate interval size (or interval width)can be found by

A)dividing sample size (N)by 10.
B)multiplying the number of categories by the lowest score.
C)dividing the range by the sample size (N).
D)dividing the range (R)by the number of categories (k).

Question 40

Table 2.2
$\begin{array}{|l|l|l|}\hline \text {TABLE 2.2 AGES OF}\\\text {RESPONDENTS}\\\hline \text { ClassIntervals } & \text { Frequency } & \text { Percentages } \\\hline 18-23 & 5 & \\\hline 2429 & 21 & \\\hline 30-40 & 10 & \\\hline \text { TOTAL } & 36 & \\\hline\\\end{array}$
If we added a cumulative percentage column to Table 2.2 and began our calculations with the 18-23 interval,the entry in the 30-40 interval would be

A)10%.
B)33.3%.
C)37%.
D)100%.

Question 41

A possible problem with open-ended or unequal intervals is that they

A)do not permit the computation of midpoints.
B)are useful only for nominal-level variables.
C)can be used only with variables that have few scores.
D)cannot be used for interval-ratio level variables.

Question 42

For a single variable measured at the nominal level,an appropriate graph would be a

A)pie chart.
B)histogram.
C)frequency polygon.
D)bivariate table.

Question 43

A line chart or frequency polygon is based on

A)the upper limits of each interval.
B)the lower limits of each interval.
C)the midpoint of each interval.
D)any limit which the researcher selects.

Question 44

Open-ended intervals

A)are always preferable to unequal intervals.
B)should never be used in actual research.
C)can be useful when there are a few very high or very low scores in a distribution.
D)should only be used with ordinal-level variables.

Question 45

The study mentioned in the text shows that monitoring and surveillance of employees

A)increased gradually until 1995 and then sharply decreased.
B)increased since 1997.
C)has been surprisingly constant since the late 1990s.
D)is virtually nonexistent in the U.S.

Question 46

Histograms and line charts or frequency polygons are used with data measured at the

A)nominal level.
B)ordinal level.
C)interval-ratio level.
D)any level.

Question 47

The frequency distribution below displays the distribution of age for a sample drawn from a community.Finish the table by completing the columns for percentages,and cumulative percentages.

Question 48

According to the study presented in the text,which of the following was the most common form of monitoring employees?

A)monitoring Internet connections
B)monitoring of computer time
C)video surveillance for security purposes
D)tapping of employee home phones

Question 49

You are the dean of students at a college and the president has asked for some information about how the student body has changed over the years.You have collected the following information regarding the number of students in various categories for two different graduating classes:

What will you say to the president when she asks:
a. What percentage of the graduating class was female in 1987? _______ 2007? _______
b. What percentage of the glass was going to graduate school in 2007? _______
Has this percentage gone up or down since 1987 and by how much? (Hint: Compute the percentage change to measure the amount of change between the two times.) _______
c. What proportion of the graduating class attended the commencement ceremony in 2007? ______
Has this proportion gone up or down since 1987, and by how much? _______
d. What proportion of the class majored in the humanities in 1987? _______ 2007? _______
e. What percent of students received financial aid in 1987? ________ 2007? _______
f. Relatively speaking, how many student finished in just four years in 1987? _______ 2007? _______
How has this percentage changed between the two years? _______
g. What proportion of students were married in 1987? _______ 2007? _______
h. Write a paragraph describing the changes in the graduating classes of 1981 and 2001.
What changes seem especially important? Why?

Question 50

Pie charts show the frequency distribution of

A)one variable.
B)two variables.
C)three or more variables.
D)any of the above

Question 51

For a single variable at the interval-ratio level,an appropriate graph would be

A)a pie chart.
B)a histogram.
C)a bivariate table.
D)None of the above.Graphs are never used for interval-ratio level variables

Question 52

Below are the scores of 25 students on a midterm test.Organize this information into a frequency distribution using a ten point grading scale for class intervals.Include columns for percentages and cumulative percentages.Write a brief description of the distribution.

Question 53

A researcher wants to visually display the U.S.divorce rate (a continuous,interval-ratio level variable)for the last 50 years.An appropriate format would be

A)a line chart or histogram.
B)only a histogram would work in this situation.
C)a pie chart.
D)None of the above.Data in the form of rate should never be displayed in a chart or graph.