To:  sbaker@odu.edu

From:  Thomas Meyer
tmeyer@ph.vccs.edu
276 656-0283
Patrick Henry Community College

Subject:  Statistics - w/  Dr.Spencer Baker - Homework Assignment #2, Ch 2 - Problem 15, page56.

Date: February 9, 2004

Question:

a.    Use the SPSS program and SPSS data bank for the data set named math.sav to obtain a frequency table for the post-instruction score on the mathematics subtest of the Iowa Test of Educational Development (ited9).

Answer:

General methodology used:

1. Have SPSS loaded onto c-drive.
2. Insert text's data disk in D-drive;
3. Double click SPSS icon;
4. Use file open and select math.sav from D-drive;

5. For this problem, select the Variable "Ited9" by clicking it;
6. Click the box which drags the variable name into the list of variables to be selected;
7. Click OK.
8. Click Analyze; choose frequencies.
9. Using the mouse, select, copy, and paste the items requested into this Frontpage and save.
10. Refresh the web page.

ITED 9th grade math score

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

45

1

2.0

2.0

2.0

52

1

2.0

2.0

4.1

58

2

4.1

4.1

8.2

59

1

2.0

2.0

10.2

60

3

6.1

6.1

16.3

61

2

4.1

4.1

20.4

63

1

2.0

2.0

22.4

65

2

4.1

4.1

26.5

66

1

2.0

2.0

28.6

67

1

2.0

2.0

30.6

69

1

2.0

2.0

32.7

70

1

2.0

2.0

34.7

71

1

2.0

2.0

36.7

72

1

2.0

2.0

38.8

73

2

4.1

4.1

42.9

75

1

2.0

2.0

44.9

76

1

2.0

2.0

46.9

78

1

2.0

2.0

49.0

79

3

6.1

6.1

55.1

80

2

4.1

4.1

59.2

81

2

4.1

4.1

63.3

83

2

4.1

4.1

67.3

84

1

2.0

2.0

69.4

85

3

6.1

6.1

75.5

86

2

4.1

4.1

79.6

88

1

2.0

2.0

81.6

89

2

4.1

4.1

85.7

90

1

2.0

2.0

87.8

91

2

4.1

4.1

91.8

95

1

2.0

2.0

93.9

96

2

4.1

4.1

98.0

97

1

2.0

2.0

100.0

Total

49

100.0

100.0

 

Question:

b1.    From the frequency table, construct a grouped cumulative frequency table. 

The main difficulty from a student's perspective is creating the score intervals correctly. 
Five guidelines are found on pages 32 and 33 of the text.  They are as follows: (with my work adapted in blue):

1. It is desirable to have each interval contain an odd number of score values.
2. As a general rule, there should be between 10 and 20 intervals in a grouped frequency distribution.

(Technique:  Subtract the lowest from the highest value.  Divide the result by interval widths of 3, 5, 7, and so on until you achieve a desirable number of intervals between 10 and 20.)

The high and low values are 97 and 45.
97-45=  52; 

Then 52/3 = 17 1/3.  So 18 intervals will do just fine.

3. All intervals should be the same width.
4.  Intervals should be selected so that they do not include impossible values.
5.  Make the interval midpoints, or one of the score limits, a multiple of the interval width.

Using a score limit of 45 and an interval width of 3 makes the lowest interval be 45-47. 
This is reflected in the table below, starting in its lower left-hand corner.
 
Midpoints are the center of each score interval. 
Frequencies are read from the table above and counted and recorded under Frequency (f).
Cumulative Frequency is the sum of Frequency (f) starting at the lower right-hand corner of the table below.

Answer: Copied from Text page 479

Score Interval

 Cumulative Midpoint
(X)
 		 Frequency
(f)		 Cumulative Frequency
(cf)
96-98 97 3 49
93-95 94 1 46
90-92 91 3 45
87-89 88 3 42
84-86 85 6 39
81-83 82 4 33
78-80 79 6 29
75-77 76 2 23
72-74 73 3 21
69-71 70 3 18
66-68 67 2 15
63-65 64 3 13
60-62 61 5 10
57-59 58 3 5
54-56 55 0 2
51-53 52 1 2
48-50 49 0 1
45-47 46 1 1
interval width
= 3		 X f cf


b2. Construct a grouped cumulative frequency curve from this table. 

See Jpeg sent via email attachment to StatHW2Ch2Prob15page56TomMeyer.



 


Question:

 

c.    Using the SPSS program, construct a grouped frequency histogram.

Answer:

 


filename: StatHW2Ch2Prob15page56TomMeyer.doc

Tom Meyer

Thomas Meyer