Deck 2: Basic Descriptive Statistics: Percentages Ratios and Rates Frequency Distributions

Question 1

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

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

Answer 1

C

Question 2

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).

Answer 2

B

Question 3

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.

Answer 3

C

Question 4

$\begin{array}{|l|l|l|}\hline \text {TABLE 2.1 POLITICAL PARTY } \\\text {MEMBERSHIP IN TWO } \\\text { COMMUNITIES } \\\hline \text { PARTY: } & \text { COMMUNITYA } & \text { COMMUUNITY B } \\\hline \text { Republican } & 103 & 17 \\\hline \text { Democrat } & 135 & 21 \\\hline \text { Independent } & 17 & 15 \\\hline \text { Socialist } & 9 & 11 \\\hline \text { TOTALS: } & 264 & 154 \\\hline\end{array}$
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 5

$\begin{array}{|l|l|l|}\hline \text {TABLE 2.1 POLITICAL PARTY } \\\text {MEMBERSHIP IN TWO } \\\text { COMMUNITIES } \\\hline \text { PARTY: } & \text { COMMUNITYA } & \text { COMMUUNITY B } \\\hline \text { Republican } & 103 & 17 \\\hline \text { Democrat } & 135 & 21 \\\hline \text { Independent } & 17 & 15 \\\hline \text { Socialist } & 9 & 11 \\\hline \text { TOTALS: } & 264 & 154 \\\hline\end{array}$
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 6

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 7

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%

Question 8

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.

Question 9

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 10

$\begin{array}{|l|l|l|}\hline \text {TABLE 2.1 POLITICAL PARTY } \\\text {MEMBERSHIP IN TWO } \\\text { COMMUNITIES } \\\hline \text { PARTY: } & \text { COMMUNITYA } & \text { COMMUUNITY B } \\\hline \text { Republican } & 103 & 17 \\\hline \text { Democrat } & 135 & 21 \\\hline \text { Independent } & 17 & 15 \\\hline \text { Socialist } & 9 & 11 \\\hline \text { TOTALS: } & 264 & 154 \\\hline\end{array}$
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 11

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 12

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 13

$\begin{array}{|l|l|l|}\hline \text {TABLE 2.1 POLITICAL PARTY } \\\text {MEMBERSHIP IN TWO } \\\text { COMMUNITIES } \\\hline \text { PARTY: } & \text { COMMUNITYA } & \text { COMMUUNITY B } \\\hline \text { Republican } & 103 & 17 \\\hline \text { Democrat } & 135 & 21 \\\hline \text { Independent } & 17 & 15 \\\hline \text { Socialist } & 9 & 11 \\\hline \text { TOTALS: } & 264 & 154 \\\hline\end{array}$
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 14

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 15

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.

Question 16

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 17

$\begin{array}{|l|l|l|}\hline \text {TABLE 2.1 POLITICAL PARTY } \\\text {MEMBERSHIP IN TWO } \\\text { COMMUNITIES } \\\hline \text { PARTY: } & \text { COMMUNITYA } & \text { COMMUUNITY B } \\\hline \text { Republican } & 103 & 17 \\\hline \text { Democrat } & 135 & 21 \\\hline \text { Independent } & 17 & 15 \\\hline \text { Socialist } & 9 & 11 \\\hline \text { TOTALS: } & 264 & 154 \\\hline\end{array}$
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 18

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

A)10.
B)100.
C)1000.
D)any of these

Question 19

$\begin{array}{|l|l|l|}\hline \text {TABLE 2.1 POLITICAL PARTY } \\\text {MEMBERSHIP IN TWO } \\\text { COMMUNITIES } \\\hline \text { PARTY: } & \text { COMMUNITYA } & \text { COMMUUNITY B } \\\hline \text { Republican } & 103 & 17 \\\hline \text { Democrat } & 135 & 21 \\\hline \text { Independent } & 17 & 15 \\\hline \text { Socialist } & 9 & 11 \\\hline \text { TOTALS: } & 264 & 154 \\\hline\end{array}$
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 20

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 21

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 these.Class intervals for interval-ratio variables do not have midpoints.

Question 22

$\begin{array}{|l|l|l|}\hline\text {TABLE 2.2 AGES OF }\\\text {RESPONDENTS }\\\hline \text { Class Intervals } & \text { Frequency } & \text { Percentages } \\\hline 18-23 & 5 & \\\hline 24-29 & 21 & \\\hline 30-40 & 10 & \\\hline \text { TOTAL } & 36 & \\\hline\end{array}$
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 23

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 24

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 25

$\begin{array}{|l|l|l|}\hline\text {TABLE 2.2 AGES OF }\\\text {RESPONDENTS }\\\hline \text { Class Intervals } & \text { Frequency } & \text { Percentages } \\\hline 18-23 & 5 & \\\hline 24-29 & 21 & \\\hline 30-40 & 10 & \\\hline \text { TOTAL } & 36 & \\\hline\end{array}$
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 26

$\begin{array}{|l|l|l|}\hline\text {TABLE 2.2 AGES OF }\\\text {RESPONDENTS }\\\hline \text { Class Intervals } & \text { Frequency } & \text { Percentages } \\\hline 18-23 & 5 & \\\hline 24-29 & 21 & \\\hline 30-40 & 10 & \\\hline \text { TOTAL } & 36 & \\\hline\end{array}$
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 27

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 28

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 29

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 30

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 31

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

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

Question 32

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 33

$\begin{array}{|l|l|l|}\hline\text {TABLE 2.2 AGES OF }\\\text {RESPONDENTS }\\\hline \text { Class Intervals } & \text { Frequency } & \text { Percentages } \\\hline 18-23 & 5 & \\\hline 24-29 & 21 & \\\hline 30-40 & 10 & \\\hline \text { TOTAL } & 36 & \\\hline\end{array}$
In Table 2.2,what proportion of cases are 18-23?

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

Question 34

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 these

Question 35

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 36

$\begin{array}{|l|l|l|}\hline\text {TABLE 2.2 AGES OF }\\\text {RESPONDENTS }\\\hline \text { Class Intervals } & \text { Frequency } & \text { Percentages } \\\hline 18-23 & 5 & \\\hline 24-29 & 21 & \\\hline 30-40 & 10 & \\\hline \text { TOTAL } & 36 & \\\hline\end{array}$
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 37

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 38

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 39

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 40

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 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

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:

Question 43

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 44

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.