Deck 2: Frequency Distributions, Percentiles,

Question 1

The lowest and highest scores are given below for different sets of scores. In each case, the scores are to be grouped into class intervals. For each, give
(1) the range,
(2) your choice of class interval width,
(3) the score limits for the lowest interval, and
(4) the score limits for the highest interval (do this directly without listing any of the intervals between the lowest and the highest):

a) 36, 62,
b) 27, 101,
c) 56, 69,
d) 187, 821,
e) 6.3, 21.9,
f) 1.27, 3.47.

Answer 1

(a) 26, 2, 36-37, 62-63?
(b)?74, 5, 25-29, 100-104 (4 or 6 also satisfactory interval sizes)?
(c)?13, 1, 56, 69?
(d)?634, 50, 150-199, 800-849 (30, 40, or 60 also satisfactory interval sizes)?
(e)?15.6, 1.0, 6.0-6.9, 21.0-21.9?
(f)?2.20, .20, 1.20-1.39, 3.40-3.59 (perhaps .10 or .15 would be satisfactory interval sizes).

Question 2

Convert the following proportions to percents (report the percent to the same degree of accuracy as the proportion):
(a)26,
(b).05,
(c).79,
(d).555,
(e).005.

Answer 2

(a) 26%
(b)5%
(c)79%
(d)55.5%
(e).5%.

Question 3

Convert the following percents to proportions (use the same degree of accuracy):
(a)42%,
(b)78%,
(c)43.7%,
(d)5.25%,
(e).8%.

Answer 3

(a)42
(b).78
(c).437
(d).0525
(e).008.

Question 4

Patrons at a local sports bar were asked to name the sport they enjoyed the most on television. The results are as follows:


(a) Construct a frequency distribution.
(b) Convert the frequencies to relative frequencies (use percentages).

Question 5

The following scores were obtained by university freshmen on an achievement test in history:
(a) Construct a grouped frequency distribution.
(b)Convert the frequencies to relative frequencies (use proportions).

Question 6

Construct a relative frequency distribution (use proportions) from the scores of the above using an interval width of 5 and 15-19 as the lowest interval.

Question 7

The director of the work-experience program at a suburban high school wants to find out the hourly wages being offered to high school students for summer jobs in the community. His secretary conducts a survey of local businesses and obtains the following results ($ per hour) for 40 different job openings:

(a) Construct a frequency distribution of the hourly wages. Use an interval width of $.20 and $3.00-$3.19 as the lowest interval. 
(b) Convert the frequencies to relative frequencies (use percentages).

Question 8

For each of the following intervals, give (1) the interval width, (2) the real limits of the interval, and (3) the apparent limits and real limits of the next higher interval (assume the scores are rounded to the nearest whole number or decimal place indicated unless otherwise specified):
(a)10-14,
(b)20-39,
(c)2.50-2.74,
(d)1.0-1.9,
(e)30-40 (accurate to the nearest 10).

Question 9

Construct a cumulative percentage distribution for the following data:

Question 10

It is claimed that class intervals should be continuous, of the same width throughout, mutually exclusive, and laid out with the highest interval placed at the top. Which characteristic, if any, is not an appropriate requirement?

A) continuity
B) of the same width
C) highest interval at the top
D) all four characteristics are highly desirable

Question 11

When scores are grouped, it is desirable to use ____________ class intervals.

A) 5-10
B) 5-20
C) 10-20
D) 15-20

Question 12

The magnitude of grouping error is

A) greatest when the number of class intervals is large
B) greatest when the number of class intervals is small
C) great when the number of class intervals is either very small or very large
D) unaffected by the number of class intervals

Question 13

John uses our guidelines to arrive at an interval size of 30. Which of the following is the most likely value for the range of scores in his sample?

A) 385
B) 210
C) 710
D) 862

Question 14

The lowest score is 23 and the highest score is 87. The range is

A) 63.0
B) 64.5
C) 64.1
D) 64.0

Question 15

The lowest score is 23 and the highest score is 87. Permissible class interval widths are

A) 3, 4, 5
B) 4, 5, 6
C) 5, 6, 7
D) 6, 7, 8

Question 16

We plan to use an interval size of 4, and 14 is the lowest score in our sample. According to our guidelines, ____________ would be the best choice for the bottom interval.

A) 14-17
B) 13-16
C) 12-15
D) 11-14

Question 17

The apparent limits of an interval are 30-34. The width of the interval is

A) 4
B) 4.5
C) 5
D) 5.5

Question 18

The real limits of the interval 50-54 are

A) 49.0-55.0
B) 49.5-54.5
C) 50.5-53.5
D) 50.0-54.0

Question 19

If measurement is to the nearest 10 lb, then a score of 540 lb means

A) 530.0-540.0 lb
B) 540.0-550.0 lb
C) 539.5-540.5 lb
D) 535.0-545.0 lb

Question 20

If we sum the values of ƒ for a frequency distribution we obtain

A) n (or N)
B) 100%
C) cum ƒ
D) cum %

Question 21

ƒ/n gives us:

A) cum ƒ
B) average frequency
C) cum %
D) relative frequency

Question 22

Twelve cases fall in the interval 40-49, and the relative frequency for that interval is .20. What is the total number of cases for the entire distribution?

A) 60
B) 48
C) 72
D) 20

Question 23

Which one, if any, of the first three alternatives is impossible?

A) a percentile has the value of 37
B) a percentile has the value of 87.4
C) a percentile has the value of 108
D) all of the above are possible

Question 24

Which one, if any, of the first three alternatives is impossible?

A) a percentile rank has the value of 37
B) a percentile rank has the value of 87.4
C) a percentile rank has the value of 108
D) all of the above are possible

Question 25

In computing percentiles from a cumulative frequency distribution, we

A) assume that the scores in an interval are represented by the upper limit of the interval
B) assume that the scores in an interval are represented by the midpoint of the interval
C) assume that the scores in an interval are spread equally throughout the interval
D) make no assumptions about the location of the scores in the interval

Question 26

Base your answers to the questions on the following distribution:


-We observe that there are six scores falling

A) below 54.5
B) at 52.0
C) above 49.5
D) between 49.5 and 54.5

Question 27

Base your answers to the questions on the following distribution:


-The score above which 12 cases fall is

A) 59.5
B) 57.0
C) 55.0
D) 54.5

Question 28

Base your answers to the questions on the following distribution:


-There are 16 scores falling below

A) 60.0
B) 59.5
C) 59.0
D) 57.0

Question 29

Base your answers to the questions on the following distribution:


-The cum ƒ value of 8 means that 8 cases fall below

A) 54.5
B) 54.0
C) 52.0
D) 49.5

Question 30

Base your answers to the questions on the following distribution:


-The score below which 40% of the cases fall is

A) 54.5
B) 54.0
C) 52.0
D) 49.5

Question 31

Base your answers to the questions on the following distribution:


-Eighty percent of the scores fall below

A) 60.0
B) 59.5
C) 59.0
D) 57.0

Question 32

Base your answers to the questions on the following distribution:


-P₄₀ is

A) 40.0
B) 55.0
C) 54.5
D) 54.0

Question 33

Base your answers to the questions on the following distribution:


-P₁₀ is

A) 10
B) 49.5
C) 47.0
D) 44.5

Question 34

Base your answers to the questions on the following distribution:


-The percentile rank of a score of 54.5 is

A) 60
B) 54.5
C) between 40 and 50
D) 40