Deck 16: Appendix: Grouped Frequency Distributions and Central Tendency

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.

Answer 1

positively skewed

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.

Answer 2

21.53.

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.

Answer 3

19

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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? $$\begin{array} { r r r r r r r r r r r r r } 12 & 24 & 6 & 9 & 9 & 20 & 13 & 14 & 17 & 20 & 23 & 13 & 9 \\10 & 7 & 11 & 14 & 12 & 38 & 22 & 13 & 7 & 28 & 20 & 33 & 15 \\6 & 33 & 16 & 11 & 9 & 5 & 21 & 26 & 15 & 14 & 9 & 8 & 13\end{array}$$

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. $$\begin{array} { r r r r r r r r r r r r r r r } 9 & 19 & 12 & 24 & 10 & 7 & 6 & 27 & 15 & 15 & 13 & 21 & 12 & 11 & 9 \\10 & 20 & 8 & 14 & 16 & 14 & 10 & 9 & 35 & 7 & 4 & 8 & 8 & 13 & 19 \\11 & 11 & 17 & 25 & 9 & 6 & 16 & 12 & 13 & 14 & 16 & 28 & & &\end{array}$$

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. $$\begin{array} { l l l l l l l l l l l l l } 38 & 22 & 27 & 41 & 37 & 13 & 33 & 35 & 31 & 36 & 36 & 32 & 40 \\31 & 40 & 35 & 34 & 24 & 36 & 30 & 18 & 25 & 37 & 27 & 30 & 34 \\35 & 38 & 37 & 28 & 34 & 19 & 37 & 32 & 29 & 33 & 21 & 26 & 31 \\38 & & & & & & & & & & & &\end{array}$$

Question 18

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

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?

Question 20

Find the median of each distribution below.

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

Question 21

Find the median of each distribution below.

- $$\begin{array} { c c } \begin{array} { r } \text { Class } \\\text { Interval }\end{array} & f \\\hline 45 - 47 & 3 \\42 - 44 & 5 \\39 - 41 & 7 \\36 - 38 & 8 \\33 - 35 & 6 \\30 - 32 & 5 \\27 - 29 & 7 \\24 - 26 & 3 \\21 - 23 & 2 \\18 - 20 & 2\end{array}$$