Question

1.         For each set below, using Excel, construct

           a.         a frequency distribution,

   b.         a relative frequency distribution, and

           c.         a cumulative relative frequency distribution.

Consider whether or not you should group your data. Describe how you determined your bin width, if you grouped the data in intervals.

Set 1 75    95    103 100 93 91 90 92 89 105 86 85 81 96 103 99 94 95 91 97 92 107 75 106 92 97 88 87 89 104 97 113 93 108 101 84 96 83 98 115 109 98 88 110 99 94 103 79 95 114 118 102 104

Set 2 82 101 89 114 128 118 105 91 100 99 113 106 106 102 95 120 97 106 103 105 112 98 85 93 107 119 104 110 97 109 100 109 95 115 83 103 90 108 83

Set 3 0    2 0 1 0 0 0 0 1 0 0 0 0 0 0 2 0 0 0 0 2 0 1 0 0 0 4 1 0 0 1 0 0 0 1 0

2. Assume that the first set of scores below represents the IQ scores of children

who have been participating in a school lunch program and the second set of scores represent the IQs of a similar group of children who have not participated in the program.

a.         Prepare appropriate graphical representations of the frequency and relative frequency distributions.

b.         Compare the two distributions by placing them on the same graph. Be sure to have equivalent intervals, if grouped. Why did you decide to compare frequencies, or relative frequencies?

3.         Assume that the third set below are data from a survey of riders of a city bus system. Each rider was asked to indicate the number of times he or she had taken a bus on a Sunday during the previous month.   Prepare a graphical representation of the relative frequency data.

Answer 1

(1)

Set 1

Class size = (Max - Min)/Number of classes = (118 - 75)/5 = 8.6 (say 10)

CI	F	Relative F	Cumulative Relative F
75 - 85	6	0.1132	0.1132
85 - 95	17	0.3208	0.4340
95 - 105	20	0.3774	0.8113
105 - 115	8	0.1509	0.9623
115 - 125	2	0.0377	1.0000
Sums =	53	1

Set 2

Class size = (Max - Min)/Number of classes = (128 - 82)/5 = 9.2 (say 10)

CI	F	Relative F	Cumulative Relative F
80 - 90	5	0.1282	0.1282
90 - 100	9	0.2308	0.3590
100 - 110	16	0.4103	0.7692
110 - 120	7	0.1795	0.9487
120 - 130	2	0.0513	1.0000
Sums =	39	1

Set 3

Here there is no need to make class intervals

X	F	Relative F	Cumulative Relative F
0	26	0.7222	0.7222
1	6	0.1667	0.8889
2	3	0.0833	0.9722
4	1	0.0278	1.0000
Sums =	36	1