Deck 2: Summarizing Data: Listing and Grouping

Question 1

A sample of 18 tries to connect to an online service using a phone line.


-The class boundaries of the second class are

A) $29.5-34.5$
B) $30-34$
C) 30-34.9
D) 29.9-34.9

Answer 1

$29.5-34.5$

Question 2

A sample of 18 tries to connect to an online service using a phone line.


-The numbers 40 and 44 are examples of

A) class marks.
B) class boundaries.
C) class limits.
D) class intervals.

Answer 2

class limits.

Question 3

A sample of 18 tries to connect to an online service using a phone line.


-The numbers 27 and 47 are examples of

A) class marks.
B) class boundaries.
C) class limits.
D) class intervals.

Answer 3

class marks.

Question 4

A sample of 18 tries to connect to an online service using a phone line.


-If a cumulative "less than" distribution were constructed from the above frequency distribution, the cumulative frequency in the third row down would be

A) 1 .
B) 9 .
C) 6 .
D) 7 .

Question 5

In a cumulative "less than" distribution, the classes are labeled using

A) class marks.
B) lower class limits.
C) upper class limits.
D) class boundaries.

Question 6

In a cumulative "more than" distribution, the classes are labeled using

A) class marks.
B) lower class limits.
C) upper class limits.
D) class boundaries.

Question 7

We can show the proportion of values falling into various class intervals by using a _______ distribution.

A) frequency
B) cumulative
C) quantitative
D) percentage

Question 8

In order to present numerical categories of a variable with their corresponding frequencies, we use a _______ distribution.

A) cumulative
B) quantitative
C) qualitative
D) percentage

Question 9

Which of the following would be a desirable property of a frequency distribution?

A) contains open end classes
B) contains more than 15 classes
C) contains exactly 4 classes
D) contains equal class intervals

Question 10

Given the frequency distribution: For the histogram of this distribution, the height of the 30-59 interval should be _______

A) 18
B) 9
C) 54
D) 6

Question 11

Table 1
A sample of 80 company employees is grouped into a table based on their weekly salaries:


-From the data in Table 1, construct a percentage distribution.

Question 12

Table 1
A sample of 80 company employees is grouped into a table based on their weekly salaries:


-From the data in Table 1, construct the cumulative "less than" distribution.

Question 13

Table 1
A sample of 80 company employees is grouped into a table based on their weekly salaries:


-From the data in Table 1, construct a cumulative "greater than" distribution.

Question 14

Table 1
A sample of 80 company employees is grouped into a table based on their weekly salaries:


-From the data in Table 1, construct a cumulative "or less" distribution.

Question 15

Solve the problem.

-Given the class marks 22, 30, 38, and 46, provide (i) class boundaries and (ii) class limits for this frequency distribution.

Question 16

Solve the problem.

-Given the class boundaries $30.95,42.95,54.95,66.95,78.95$ , provide (i) class limits and (ii) class marks for this frequency distribution.

Question 17

The following are three daily pizza sales in units for a local pizza restaurant for the past two weeks: $228,252,310,305,165,182,312,182,171,285,307,281,234,175$

-For this data, construct a stem-and-leaf display with the stem labels 1, 2, and 3 (and, hence, with two-digit leaves).

Question 18

The following are three daily pizza sales in units for a local pizza restaurant for the past two weeks: $228,252,310,305,165,182,312,182,171,285,307,281,234,175$

-For this data, construct a stem-and-leaf display with one-digit leaves.

Question 19

To group data on the number of potential buyers entering an automobile dealer's showroom for a given week, the sales manager uses the classes $25-49,51-75,75-99,100-124$ , and 125-149. Explain what difficulties might arise.

Question 20

In a graph of frequency distribution with classes 10-19, 20-29, 30-59, and 60-69, explain why a histogram of the data might be misleading if all the heights of the rectangles are equal to the class frequencies.

Question 21

List the data which correspond to the following stem-and-leaf display.
$3 \lvert \begin{array}{lllllll}6 & 2 & 5 & 7 & 2\end{array}$

Question 22

List the data which correspond to the following stem-and-leaf display.
$4 \left\lvert\, \begin{array}{lllll}72 & 51 & 36 & 23 & 95\end{array}\right.$

Question 23

The Highway Patrol, using radar, checked the speeds (in $\mathrm{mph}$ ) of 30 passing motorists at a checkpoint. The results are listed below. Construct a dot diagram for the data.

Question 24

The heights (in inches) of 30 adult males are listed below. Construct a dot diagram for the data.
$\begin{array}{llllllllll}70 & 72 & 71 & 70 & 69 & 73 & 69 & 68 & 70 & 71\end{array}$
$\begin{array}{llllllllll}67 & 71 & 70 & 74 & 69 & 68 & 71 & 71 & 71 & 72\end{array}$
$\begin{array}{llllllllll}69 & 71 & 68 & 67 & 73 & 74 & 70 & 71 & 69 & 68\end{array}$

Question 25

At a dairy products convention, an interviewer asked 40 persons to name their favorite dairy product. Their replies were ice cream, butter, cheese, butter, butter, milk, butter, sour cream, ice cream, cheese, butter, cheese, milk, cheese, butter, cheese, ice cream, butter, milk, butter, sour cream, ice cream, cheese, milk, butter, ice cream, cheese, butter, milk, sour cream, butter, cheese, milk, butter, cheese, milk, ice cream, sour cream, ice cream, and ice cream. Draw a bar chart with vertical bars for these categorical data.

Question 26

In a software engineering class, the professor asked 48 students to name their favorite programming language. Their replies were Java, Perl, Perl, C++, Java, Lisp, Perl, Java, C++, Perl, Perl, Java, Smalltalk, Perl, Java, C++, Perl, Lisp, Perl, Perl, Java, Java, C++, Perl, Smalltalk, C++, Perl, Java, Lisp, Java, Perl, Perl, Perl, Smalltalk, C++, Java, Lisp, Perl, Java, Lisp, Java, Perl, Smalltalk, Java, Lisp, C++, Java, and Perl. Draw a bar chart with vertical bars for these categorical data.

Question 27

A study was conducted to determine how people get jobs. Four hundred subjects were randomly selected and the results are listed below.
Construct a Pareto diagram in the form of a bar chart for the data. (Remember, in a Pareto diagram, the data is arranged in descending order.)

Question 28

The heights (in inches) of 30 adult males are listed below. Construct a Pareto diagram in the form of a bar chart for the data. (Remember, in a Pareto diagram, the data is arranged in descending order.)
$\begin{array}{llllllllll}70 & 72 & 71 & 70 & 69 & 73 & 69 & 68 & 70 & 71\end{array}$
$\begin{array}{llllllllll}67 & 71 & 70 & 74 & 69 & 68 & 71 & 71 & 71 & 72\end{array}$
$\begin{array}{llllllllll}69 & 71 & 68 & 67 & 73 & 74 & 70 & 71 & 69 & 68\end{array}$

Question 29

For the data below, construct a frequency histogram and a frequency polygon.

Question 30

For the data below, construct a frequency histogram and a frequency polygon.

Question 31

The grade point averages for 40 students are listed below. Construct a frequency histogram and a frequency polygon using eight classes.
$\begin{array}{llllllllll}2.0 & 3.2 & 1.8 & 2.9 & 0.9 & 4.0 & 3.3 & 2.9 & 3.6 & 0.8\end{array}$
$\begin{array}{llllllllll}3.1 & 2.4 & 2.4 & 2.3 & 1.6 & 1.6 & 4.0 & 3.1 & 3.2 & 1.8\end{array}$
$\begin{array}{llllllllll}2.2 & 2.2 & 1.7 & 0.5 & 3.6 & 3.4 & 1.9 & 2.0 & 3.0 & 1.1\end{array}$
$\begin{array}{llllllllll}3.0 & 4.0 & 4.0 & 2.1 & 1.9 & 1.1 & 0.5 & 3.2 & 3.0 & 2.2\end{array}$

Question 32

The heights (in inches) of 30 adult males are listed below. Construct a frequency histogram using five classes.
$\begin{array}{llllllllll}70 & 72 & 71 & 70 & 69 & 73 & 69 & 68 & 70 & 71\end{array}$
$\begin{array}{llllllllll}67 & 71 & 70 & 74 & 69 & 68 & 71 & 71 & 71 & 72\end{array}$
$\begin{array}{llllllllll}69 & 71 & 68 & 67 & 73 & 74 & 70 & 71 & 69 & 68\end{array}$

Question 33

The heights (in inches) of 30 adult males are listed below. Construct a frequency polygon using five classes.
$\begin{array}{llllllllll}70 & 72 & 71 & 70 & 69 & 73 & 69 & 68 & 70 & 71\end{array}$
$\begin{array}{llllllllll}67 & 71 & 70 & 74 & 69 & 68 & 71 & 71 & 71 & 72\end{array}$
$\begin{array}{llllllllll}69 & 71 & 68 & 67 & 73 & 74 & 70 & 71 & 69 & 68\end{array}$

Question 34

For the data below, construct an ogive.

Question 35

For the data below, construct an ogive.

Question 36

For the data below, construct an ogive.

Question 37

For the data below, construct an ogive.

Question 38

A study was conducted to determine how people get jobs. Four hundred subjects were randomly selected and the results are listed below.
Construct a pie chart of the data.

Question 39

The grade point averages for 40 students are listed below. Construct an ogive using eight classes.
$\begin{array}{llllllllll}2.0 & 3.2 & 1.8 & 2.9 & 0.9 & 4.0 & 3.3 & 2.9 & 3.6 & 0.8\end{array}$
$\begin{array}{llllllllll}3.1 & 2.4 & 2.4 & 2.3 & 1.6 & 1.6 & 4.0 & 3.1 & 3.2 & 1.8\end{array}$
$\begin{array}{llllllllll}2.2 & 2.2 & 1.7 & 0.5 & 3.6 & 3.4 & 1.9 & 2.0 & 3.0 & 1.1\end{array}$
$\begin{array}{llllllllll}3.0 & 4.0 & 4.0 & 2.1 & 1.9 & 1.1 & 0.5 & 3.2 & 3.0 & 2.2\end{array}$

Question 40

The heights (in inches) of 30 adult males are listed below. Construct a ogive using five classes.
$\begin{array}{llllllllll}70 & 72 & 71 & 70 & 69 & 73 & 69 & 68 & 70 & 71\end{array}$
$\begin{array}{llllllllll}67 & 71 & 70 & 74 & 69 & 68 & 71 & 71 & 71 & 72\end{array}$
$\begin{array}{llllllllll}69 & 71 & 68 & 67 & 73 & 74 & 70 & 71 & 69 & 68\end{array}$

Question 41

The Highway Patrol, using radar, checked the speeds (in mph) of 30 passing motorists at a checkpoint. The results are listed below. Construct an ogive using six classes.

Question 42

In a study of the growth of termite hills in the desert, an experiment was performed to determine how well the height of such hills can be determined from aerial photographs. Following are the heights of 36 termite hills (in centimeters) estimated from aerial photographs, $x$ , and measured on the ground, $y$ :
Produce a two-way frequency distribution with the classes 200-219, 220-239, 240-259, 260-279, and 280-299 for both variables.

Question 43

Following are the numbers of minutes it took 27 students to memorize two lists of German adjectives, one in the morning and one in the late afternoon.
Produce a two-way frequency table for these data using the classes 10-14, 15-19, 20-24, and 25-29 for the morning, and the classes 15-19, 20-24, and 25-29 for the afternoon.

Question 44

One of the advantages of frequency distributions is that we can find the exact highest value in the data.

Question 45

The sum of the frequencies in a frequency distribution is equal to the number of elements in the sample.

Question 46

An ogive of a cumulative "less than" distribution always decreases as we move from left to right.

Question 47

For a frequency distribution, we can never find the total of all the original scores.

Question 48

It is possible for the class boundaries of an interval to be the same as its class limits.

Question 49

A frequency polygon is a line graph of a cumulative frequency distribution.

Question 50

A stem-and-leaf display contains no more information than a frequency distribution.

Question 51

A frequency distribution always has equal class intervals.

Question 52

Frequency distributions are of two types: quantitative and qualitative.

Question 53

If two consecutive class intervals of a frequency distribution are 60-67 and 68-75, the class boundaries of the second interval are 68.95-75.95.

Question 54

In constructing a frequency distribution from raw data, there will usually be between _______ and _______ classes.

Question 55

The single number that best represents a given interval of a frequency distribution is called the _______.

Question 56

In a stem-and-leaf display, each digit to the right of the vertical line is called a _______.

Question 57

Pie charts are graphical representations of _______ distributions.

Question 58

If categories of a distribution differ in kind rather than degree, the resulting table is called a _______.

Question 59

A bar chart of a frequency distribution is called a _______.

Question 60

A class mark is defined as the average of _______

Question 61

A class interval can be defined as a _______

Question 62

For an ogive, the horizontal axis should contain the class _______

Question 63

A numerical distribution is the same as a _______ distribution.