12. Explain and give an example for each of the following types of
variables: (a) equal-interval, (b) rank-order, (c) nominal, (d) ratio scale,
(e) continuous.
(a) An equal-interval variable is variable by which numbers
represent numbers stand for almost exact equal amounts of what is being
measured (Aron, Aron, & Coups, 2009). An example is the difference between
stress ratings of 2 and 4 means about as much as the difference between 5 and 7.
(b) A rank-order or ordinal variables is a variable by which numbers stand for
relative ranking only (Aron, Aron, & Coups, 2009). An example is a car
models’ standing in a safety class ranking. (c) Nominal variable is a variable
by which the values are categories or names (Aron, Aron, & Coups, 2009). An
example is the nominal variable student; the values are traditional and
nontraditional. (d) A ratio scale is a scale of measurement of data, which
allows comparisons of the differences of values. An example is the time
measured from the "Big Bang" until present is on a ratio scale,
because before the “Big Bang” time had not begun on Earth. (e) Aron, Aron, and
Coups (2009), “with a continuous variable, there are in theory an infinite
number of values between any two values” (p. 4). An example is measuring height
because the variables would be continuous. There are an unlimited number of
possibilities of height even when only looking at between 4 and 5.2 feet.
15. Following are the speeds of 40 cars clocked by radar on a
particular road in an 35-mph zone on a particular afternoon:
30, 36, 42, 36, 30, 52, 36, 34, 36, 33, 30, 32, 35, 32, 37, 34,
36, 31, 35, 20,
24, 46, 23, 31, 32, 45, 34, 37, 28, 40, 34, 38, 40, 52, 31, 33,
15, 27, 36, 40
Make (a) a frequency table and (b) a histogram. Then (c) describe
the general shape of the distribution.
(a)
Frequency Table
|
SPEED
|
FREQUENCY
|
PERCENTAGE
|
|
15-19
|
1
|
2.5
|
|
20-24
|
3
|
7.5
|
|
25-29
|
2
|
5
|
|
30-34
|
15
|
37.5
|
|
35-39
|
11
|
27.5
|
|
40-44
|
4
|
10
|
|
45-49
|
2
|
5
|
|
50-54
|
2
|
5
|
(b) Histogram
(c) The general shape of distribution is unimodal.
19. Give an example of something having these distribution shapes:
(a) bimodal, (b) approximately rectangular, and (c) positively skewed. Do not
use an example given in this book or in class.
(a) Bimodal: an example is a day’s account of new drivers taken
the written examination driver test. The majority of participants scored
between 85-98%, the second largest category of participants scored between 84-88%,
and the remainder of participants scored inconsistently between 55% and 99%.
(b) Approximately rectangular: an example is an online college
classroom of 25 traditional and nontraditional students. 15 of the students
were 19 years of age and 10 were 32 years of age, which generates a rectangular
distribution.
(c) Positively skewed: an
example is a case study of 25 college seniors, whereas one computes the hours
of study spent on coursework daily, which may show positively skewed
distribution. In this case study 10 students spent 2-3 hours studying daily, 11
spent 3 hours studying daily, and 3 students spent 4-5 hours studying daily.
Giving outcomes positively skewed.
20. Find an example in a newspaper or magazine of a graph that
misleads by failing to use equal interval sizes or by exaggerating proportions.
This graph shows the stock market plummeted the day after President
Barack Obama’s re-election but it does not show the trend of losses before the
President’s re-election. The plummet started on May, 2008, which is not
indicated. This leads individuals to believe the drop resulted from President Barack
Obama’s re-election.
21. Nownes (2000) surveyed representatives of interest groups who
were registered as lobbyists of three U.S. state legislatures. One of the
issues he studied was whether interest groups are in competition with each
other. Table 1–10 shows the results for one such question. (a) Using this table
as an example, explain the idea of a frequency table to a person who has never
had a course in statistics. (b) Explain the general meaning of the pattern of
results.
(a) Frequency tables are used to explain data gathered and are a way
to display certain factors present. These tables are used to find the mean of a
large set of data values. In table 1-10, what is demonstrated is what the
specific group encounters competition. 20% experiences no competition, 58%
experiences some competition, and 22% experiences a lot of competition. (b) The
general meaning of the pattern of results from table 1-10, shows results split up
exhibiting a specific frequency of a group which encounters rivalry from
similar groups. All responses are represented in percentage and number patterns,
which indicate the relationship occurring between the groups.
22. Mouradian (2001) surveyed college students selected from a
screening session to include two groups: (a) “Perpetrators”—students who
reported at least one violent act (hitting, shoving, etc.) against their
partner in their current or most recent relationship—and (b)
“Comparisons”—students who did not report any such uses of violence in any of
their last three relationships. At the actual testing session, the students
first read a description of an aggressive behavior such as, “Throw something at
his or her partner” or “Say something to upset his or her partner.” They then
were asked to write “as many examples of circumstances of situations as [they
could] in which a person might engage in behaviors or acts of this sort with or
towards their significant other.” Table 1–11 shows the “Dominant Category of
Explanation” (the category a participant used most) for females and males,
broken down by comparisons and perpetrators. (a) Using this table as an
example, explain the idea of a frequency table to a person who has never had a
course in statistics. (b) Explain the general meaning of the pattern of
results.
(a) The information in the frequency table explains by sorting the
data briefly and clearly. The table exhibits frequency and the percentage of occurrences
team members, male and female experienced in each category situation.
(b) The general meaning of the results shows the trend of outcomes
for the table, whereas the majority of women perpetrators (27%) display
intimate aggression because of control motives, and the majority of men perpetrators
(31%) display expressive aggression. The combined majority of intimate aggression
of men and women was rejection of perpetrator or act with 46%, and the combined
lowest of intimate aggression of men and women was prosocial/acceptable
explanations with 0%.
Clark, P. (2012). The New York Observer. Retrieved from
http://observer.com/2012/11/stocks-fall-on-day-after-obama-reelection-but-not-as-far-as-in-2008/
