Question 1

Data Set B-1: $$\begin{array} { c c } 
\text { Class Interval } & f \
33 - 35 & 1 \
30 - 32 & 0 \
27 - 29 & 2 \
24 - 26 & 3 \
21 - 23 & 2 \
18 - 20 & 8 \
15 - 17 & 3
\end{array}$$
-The distribution in Data Set B-1 is
A) positively skewed
B) negatively skewed
C) violates the convention that the lowest class interval start with a multiple of i
D) none of the other alternatives are correct.

Accepted Answer

The distribution is positively skewed because the frequency decreases as the class intervals increase, indicating a longer tail on the right side.

Question 2

Data Set B-1: $$\begin{array} { c c } 
\text { Class Interval } & f \
33 - 35 & 1 \
30 - 32 & 0 \
27 - 29 & 2 \
24 - 26 & 3 \
21 - 23 & 2 \
18 - 20 & 8 \
15 - 17 & 3
\end{array}$$
-The mean of Data Set B-1 is
A) 23.16
B) 22.53
C) 20.53
D) 21.53.

Accepted Answer

D

Question 3

Data Set B-1: $$\begin{array} { c c } 
\text { Class Interval } & f \
33 - 35 & 1 \
30 - 32 & 0 \
27 - 29 & 2 \
24 - 26 & 3 \
21 - 23 & 2 \
18 - 20 & 8 \
15 - 17 & 3
\end{array}$$
-The median of Data Set B-1 is
A) 8
B) 9.5
C) 19
D) 26.5.

Accepted Answer

The median of a dataset is the middle value when the data is arranged in ascending order. For grouped data, the median class is the class interval that contains the median. To find the median class, we calculate the cumulative frequency and then find the class that contains the middle value. The total number of observations (N) is 1 + 0 + 2 + 3 + 2 + 8 + 3 = 19. Half of this is 9.5, so we look for the class interval that contains the 9.5th observation. The cumulative frequencies are 1, 1, 3, 6, 8, 16, 19. The 18 - 20 class interval is the median class because it contains the 9.5th observation. Since the class interval is 18 - 20, the median cannot be a specific value like 19 without further calculation, but it indicates that the median falls within this range. Therefore, the choice that corresponds to the median class interval is the correct answer.

Question 4

Data Set B-1: $$\begin{array} { c c } 
\text { Class Interval } & f \
33 - 35 & 1 \
30 - 32 & 0 \
27 - 29 & 2 \
24 - 26 & 3 \
21 - 23 & 2 \
18 - 20 & 8 \
15 - 17 & 3
\end{array}$$
-The mode of Data Set B-1 is
A) 8
B) 18
C) 20
D) none of the other alternatives are correct.

Accepted Answer

The answer of Data Set B-1: \[\begin{array} { c c...

Question 5

For grouped frequency distributions with i = 10 or fewer, the number of scores covered by a class interval should be
A) even
B) odd
C) either even or odd are equally acceptable
D) a multiple of 5.

Accepted Answer

The answer of For grouped frequency distributions with i =...

Question 6

In a grouped frequency distribution, which of the following number of class intervals is considered acceptable by your text?
A) 3
B) 5
C) 10
D) all of the other alternatives are correct.

Accepted Answer

The answer of In a grouped frequency distribution, which of...

Question 7

Which statement is incorrect?
A) There should be not fewer than 10 or more than 20 class intervals.
B) The size of class intervals (i) should be an even number or a multiple of 10.
C) Each class interval should begin with a multiple of i.
D) none of the other alternatives are correct.

Accepted Answer

The size of class intervals does not necessarily need to be an even number or a multiple of 10. The choice of class interval size depends on the data set and the level of detail required for the analysis.

Question 8

If the lowest and highest scores in a distribution were 112 and 245, an appropriate class interval size would be
A) 5
B) 10
C) 20
D) none of the other alternatives are correct.

Accepted Answer

The answer of If the lowest and highest scores in...

Question 9

In a grouped frequency distribution
A) the number of class intervals should be 8-12
B) class intervals should begin with a multiple of i
C) low scores go at the top of the table
D) all of the other alternatives are correct.

Accepted Answer

The answer of In a grouped frequency distribution
A) the number...

Question 10

In a population of 150 scores, the largest score is 85 and the smallest 12. If these data are organized into a grouped frequency distribution, i will be
A) 3
B) 4
C) 5
D) 10.

Accepted Answer

The range of the data is 85 - 12 = 73. A common method for determining the number of classes (i) in a frequency distribution is to use Sturges' formula, which is i = 1 + 3.322 log N, where N is the number of observations. For N = 150, this gives i ≈ 1 + 3.322 log(150) ≈ 8. However, since this specific question does not provide a clear method for determining i and the options given do not include 8, the next best approach is to consider the context and the options provided. Without a specific formula or method indicated in the question, and given the options available, it's not possible to directly apply a standard rule to choose among the provided options (A, B, C, D). Therefore, the correct answer is chosen based on the assumption that a typical approach or a reasonable number of classes for a dataset of this size might be sought, which often falls into the range of 5 to 20 classes for practical purposes. However, without additional context or a specified method for determining i, the selection of "C) 5" is based on a common approach to data organization rather than a strict calculation.

Question 11

If there were 21 scores below the interval 3-5, 9 scores in the interval, and 16 scores above the interval 3-5, the median would be
A) 21
B) 6
C) 9
D) 4.

Accepted Answer

The median is the middle value of a data set. With 21 scores below, 9 scores in the interval, and 16 scores above, there are a total of 46 scores. The median is the 23rd score, which falls in the interval 3-5. Since the interval is 3-5, the median is 4.

Question 12

Suppose there were 21 scores above the interval 51 to 59, 6 scores in the interval, and 18 scores below the interval. The median would be
A) 21
B) 18
C) 6
D) none of the other alternatives are correct.

Accepted Answer

The total number of scores is 21 (above) + 6 (in the interval) + 18 (below) = 45. The median is the middle value, so it would be the 23rd score when arranged in order. Given the intervals, the 23rd score falls within the scores above the interval 51 to 59, not within the options given as A, B, or C.

Question 13

Suppose there were 65 scores above the interval 55-59, 9 scores in the interval and 62 scores below the interval. The median would be:
A) 57
B) 59
C) 62
D) 65.

Accepted Answer

The median is the middle score when all scores are arranged in ascending order. With 65 scores above and 62 scores below the interval 55-59, the median must fall within this interval. Since the exact value within the interval isn't specified, the closest we can approximate is the middle of the interval, which is 57.

Question 14

Suppose there were 10 scores in the interval 45-49. In the intervals above this one there were 30 scores and in the intervals below there were 26 scores. The median for this distribution would be
A) 10
B) 26
C) 45
D) 49
E) none of the other alternatives are correct.

Accepted Answer

The median is the middle score when all scores are arranged in ascending order. Given there are 10 scores in the 45-49 interval, 30 scores above, and 26 below, the total number of scores is 66. The median would fall within the 45-49 interval because the 33rd and 34th scores (the middle scores for an even number of total scores) would be within the 10 scores of the 45-49 interval, not at the specific values of 10, 26, 45, or 49.

Question 15

A psychology professor believed he should know what assumptions, prejudices, and knowledge students begin the introductory psychology course with. Accordingly, over the years he had given a 40-item true-false test on the first day of class to help himself orient to the new class. On the first day everyone was in class and the following scores were obtained. Arrange them into a grouped frequency distribution. The smallest interval is 3-5 and the largest is 36-38. From the grouped frequency distribution find the mean, median, and mode. Graph the data using the appropriate method. If the data are skewed, tell the direction. Are these data a population or a sample? $$\begin{array} { r r r r r r r r r r r r r } 
12 & 24 & 6 & 9 & 9 & 20 & 13 & 14 & 17 & 20 & 23 & 13 & 9 \
10 & 7 & 11 & 14 & 12 & 38 & 22 & 13 & 7 & 28 & 20 & 33 & 15 \
6 & 33 & 16 & 11 & 9 & 5 & 21 & 26 & 15 & 14 & 9 & 8 & 13
\end{array}$$

Accepted Answer

The answer of A psychology professor believed he should know...

Question 16

A student arrived on campus in September to find that dorm charges had gone up. Observing that there had been no capital improvements in his room or in the dorm, and knowing that mortgage rates could not be involved (the dorm had been paid off for 35 years), he inquired politely at the business office about the reasons for the increase. "Utilities went up,"was the answer. Having an activist upbringing, he planned an energy conservation campaign designed to turn out unused lights. In order to have convincing data for the college business office, he first measured the number of lights that were on but not being used in each of the six dorms on campus. These pre-campaign observations were made every night at 10 P.M. for a week and are shown below.
a. Arrange them into an appropriate frequency distribution.
b. Draw a graph of the distribution.
c. Find the mean of the distribution.
d. Find the median of the distribution.
e. Describe the direction of the skew, if any.
f. Are answers c and d parameters or statistics? Justify your answer. $$\begin{array} { r r r r r r r r r r r r r r r } 
9 & 19 & 12 & 24 & 10 & 7 & 6 & 27 & 15 & 15 & 13 & 21 & 12 & 11 & 9 \
10 & 20 & 8 & 14 & 16 & 14 & 10 & 9 & 35 & 7 & 4 & 8 & 8 & 13 & 19 \
11 & 11 & 17 & 25 & 9 & 6 & 16 & 12 & 13 & 14 & 16 & 28 & & &
\end{array}$$

Accepted Answer

The answer of A student arrived on campus in September...

Question 17

The new governor, steadily dropping in popularity, decided that her only hope was to be perceived as a tough, no-nonsense guy. She held a press conference and declared that state budgets would be "cut to the bone."The director of meat inspection, fearful of the consequences of having his budget quartered, decided to beef up all requests with as many numbers as he could muster. To support the request for new cars, he asked a hireling to make up a chart of the agency's automobile odometer readings. The numbers below represent those readings in thousands of miles. Be that hireling and arrange them into a frequency distribution using intervals of 12-14 to 39-41. Find the mean, median and mode. Graph the data using an appropriate graph. Tell the direction of skew, if any. Finally, do these data constitute a population or a sample? Justify your answer. $$\begin{array} { l l l l l l l l l l l l l } 
38 & 22 & 27 & 41 & 37 & 13 & 33 & 35 & 31 & 36 & 36 & 32 & 40 \
31 & 40 & 35 & 34 & 24 & 36 & 30 & 18 & 25 & 37 & 27 & 30 & 34 \
35 & 38 & 37 & 28 & 34 & 19 & 37 & 32 & 29 & 33 & 21 & 26 & 31 \
38 & & & & & & & & & & & &
\end{array}$$

Accepted Answer

The answer of The new governor, steadily dropping in popularity,...

Question 18

Write an appropriate set of class intervals that could be used for a grouped frequency distribution for the scores below. $$\begin{array} { l l l l l l l l l l l l l } 
28 & 68 & 54 & 47 & 39 & 52 & 71 & 16 & 18 & 39 & 70 & 44 & 39 \
27 & 31 & 62 & 48 & 53 & 37 & 21 & 47 & 62 & 12 & 28 & 21 & 47 \
52 & 74 & 29 & 69 & 25 & 68 & 11 & 55 & 72 & 36 & 50 & 44 & 47 \
49 & 62 & 57 & 39 & 21 & 42 & 57 & 69 & 75 & 19 & 60 & 47 & 35 \
55 & 61 & 43 & 72 & 61 & 27 & 43 & 50 & & & & &
\end{array}$$

Accepted Answer

The answer of Write an appropriate set of class intervals...

Question 19

The following are numbers of bar-press responses recorded for a group of 40 rats during extinction training, when no bar presses are reinforced. $$\begin{array} { l l l l l l l l l l l l l } 
49 & 41 & 38 & 53 & 46 & 30 & 33 & 50 & 43 & 28 & 27 & 39 & 44 \
36 & 56 & 44 & 42 & 37 & 35 & 48 & 45 & 32 & 40 & 25 & 30 & 26 \
47 & 40 & 37 & 34 & 37 & 42 & 47 & 39 & 45 & 40 & 34 & 43 & 41 \
36 & & & & & & & & & & & &
\end{array}$$ 
a. Set up an appropriately grouped frequency distribution.
b. From your grouped frequency distribution, find thei. mean ii. median iii. mode
c. For these data, which measure of central value is most appropriate? Why?

Accepted Answer

The answer of The following are numbers of bar-press responses...

Question 20

Find the median of each distribution below.
-$$\begin{array} { c c } 
\text { Class } & f \
\text { Interval } & \
\hline 73 - 77 & 2 \
68 - 72 & 3 \
63 - 67 & 5 \
58 - 62 & 7 \
53 - 57 & 8 \
48 - 52 & 8 \
43 - 47 & 7 \
38 - 42 & 4 \
33 - 37 & 2 \
28 - 32 & 1
\end{array}$$

Accepted Answer

The answer of Find the median of each distribution below.
-\[\begin{array}...

Quiz 16: Appendix: Grouped Frequency Distributions and Central Tendency

Data Set B-1: $\begin{array} { c c } \text { Class Interval } & f \\33 - 35 & 1 \\30 - 32 & 0 \\27 - 29 & 2 \\24 - 26 & 3 \\21 - 23 & 2 \\18 - 20 & 8 \\15 - 17 & 3\end{array}$ -The distribution in Data Set B-1 is

Data Set B-1: $\begin{array} { c c } \text { Class Interval } & f \\33 - 35 & 1 \\30 - 32 & 0 \\27 - 29 & 2 \\24 - 26 & 3 \\21 - 23 & 2 \\18 - 20 & 8 \\15 - 17 & 3\end{array}$ -The mean of Data Set B-1 is

Data Set B-1: $\begin{array} { c c } \text { Class Interval } & f \\33 - 35 & 1 \\30 - 32 & 0 \\27 - 29 & 2 \\24 - 26 & 3 \\21 - 23 & 2 \\18 - 20 & 8 \\15 - 17 & 3\end{array}$ -The median of Data Set B-1 is

Data Set B-1: $\begin{array} { c c } \text { Class Interval } & f \\33 - 35 & 1 \\30 - 32 & 0 \\27 - 29 & 2 \\24 - 26 & 3 \\21 - 23 & 2 \\18 - 20 & 8 \\15 - 17 & 3\end{array}$ -The mode of Data Set B-1 is

For grouped frequency distributions with i = 10 or fewer, the number of scores covered by a class interval should be

In a grouped frequency distribution, which of the following number of class intervals is considered acceptable by your text?

Which statement is incorrect?

If the lowest and highest scores in a distribution were 112 and 245, an appropriate class interval size would be

In a grouped frequency distribution

In a population of 150 scores, the largest score is 85 and the smallest 12. If these data are organized into a grouped frequency distribution, i will be

If there were 21 scores below the interval 3-5, 9 scores in the interval, and 16 scores above the interval 3-5, the median would be

Suppose there were 21 scores above the interval 51 to 59, 6 scores in the interval, and 18 scores below the interval. The median would be

Suppose there were 65 scores above the interval 55-59, 9 scores in the interval and 62 scores below the interval. The median would be:

Suppose there were 10 scores in the interval 45-49. In the intervals above this one there were 30 scores and in the intervals below there were 26 scores. The median for this distribution would be

Find the median of each distribution below. - $\begin{array} { c c } \text { Class } & f \\\text { Interval } & \\\hline 73 - 77 & 2 \\68 - 72 & 3 \\63 - 67 & 5 \\58 - 62 & 7 \\53 - 57 & 8 \\48 - 52 & 8 \\43 - 47 & 7 \\38 - 42 & 4 \\33 - 37 & 2 \\28 - 32 & 1\end{array}$