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Statistics for the Behavioral Sciences, 4/e

Michael Thorne, Mississippi State University -- Mississippi State
Martin Giesen, Mississippi State University -- Mississippi State

The Frequency Distribution

Problems

A group of students is given four brief presentations of a list of 15 nouns. A recognition test is given after a 20-minute delay. The number of nouns correctly identified by each student is listed next. Arrange them into a frequency distribution. Include a Cum f column and a Cum %age column.
6 15 12
8 15 14
12 13 13
15 15 13
13 10 15
Another group of students is given similar exposure to the same list of 15 nouns but is given a recall test rather than a recognition test of retention. The resulting scores are listed here. Construct a frequency distribution. Why would it be unnecessary to convert the frequencies in Problems 1 and 2 to percentages if you wanted to compare the two distributions?
0 1 2
1 1 4
0 2 2
0 1 1
3 2 1
To test their reaction times, 50 students from an introductory psychology class are asked to press a button when a green light flashes on. Their reaction times in hundredths of a second are as follows:
25 33 28 22 18
31 23 29 25 15
17 21 27 37 16
19 19 25 30 25
15 18 18 26 24
16 21 17 21 23
16 20 15 15 23
17 17 14 16 25
25 15 20 17 26
24 12 21 19 20
1. Construct a frequency distribution.
2. Add the real limits and a %age frequency column to your frequency distribution.
Find the real limits for each of the following scores:
Apparent Limits Real Limits
a. 25
b. 11.7
c. 12.55
d. 7.853
A random sample of 20 depressive patients has been given the MMPI. Their scores on Scale 2 (Depression Scale) are as follows:
30 25 26 31
45 37 35 36
32 32 30 26
28 34 34 42
33 32 35 39
Construct a frequency distribution. Include a Cum f column and a %age f column.

For practice, some graduate students in a personality appraisal course administer the MMPI to 85 of their friends. Their scores on Scale 4 (Psychopathic Deviate) are shown in frequency distribution A as follows. Distribution B shows the Scale 4 results from 32 participants in a DWI (Driving While Intoxicated) class. What would you have to do to the frequency distributions in order to compare them? Add the appropriate column to each distribution.

Distribution A		Distribution B
X	f	X	f

79	1	79	1
77	1	78	2
76	1	77	2
74	2	76	2
65	2	75	3
64	3	74	2
62	2	73	2
60	2	71	1
57	5	70	2
56	4	69	3
54	6	68	4
53	7	65	1
52	6	60	1
51	7	58	2
50	10	55	1
49	7	50	1
48	6	44	1
47	4	39	1
45	2
44	1
42	3
40	2
39	1

A large number of students took a 50-item test in a section of introductory psychology. A frequency distribution of the results is shown here. Show the real limits, cumulative frequencies, and cumulative percentages. What is N?
X f X f

49 1 35 8
48 6 34 3
47 6 33 1
46 11 32 7
45 13 31 3
44 16 30 4
43 8 29 3
42 15 28 4
41 16 27 1
40 13 26 3
39 9 25 2
38 5 23 1
37 3
36 7

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