Math 220_ Project 3
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School
James Madison University *
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Course
220
Subject
Statistics
Date
Feb 20, 2024
Type
Pages
3
Uploaded by mahek92811
IQ scores for boys and girls.
Here are the IQ test scores of 31 seventh-grade girls in a Midwest
school district:
114
100
104
89
102
91
114
114
103
105
108
130
120
132
111
128
118
119
86
72
111
103
74
112
107
103
98
96
112
112
93
The IQ test scores of 47 seventh-grade boys in the same district are
111
107
100
107
115
111
97
112
104
106
113
109
113
128
128
118
113
124
127
136
106
123
124
126
116
127
119
97
102
110
120
103
115
93
123
79
119
110
110
107
105
105
110
77
90
114
106
(a) How many variables are there? Classify them.
There are 2 variables in this study, IQ and gender. IQ is quantitative discrete, and gender is
qualitative nominal.
(b) Describe the distribution of IQ scores for all students.
Girls:
-
Mean: 105.8387
-
Min: 72.00
-
Q1: 98.000
-
Median: 107.00
-
Q3: 114.0000
-
Max: 132.00
-
Range: 60.00
-
Standard Deviation: 14.2714
-
IQR: 16.00
-
Shape: skewed to left
Boys:
-
Mean: 110.9574
-
Min: 77.00
-
Q1: 105.0000
-
Median: 111
-
Q3: 119.000
-
Max: 136.00
-
Range: 59.00
1
-
Standard Deviation: 12.1207
-
IQR: 14.00
-
Shape: skewed to left
Overall Outliers:
72.00, 74.00, 77.00, 79.00
(c)
Compare and contrast the distribution of IQ scores by gender, using
numerical and
graphical
summaries.
For starters, looking at the data, the data set for males is ⅓ bigger than the females,
having 47 samples compared to the 31 samples the women has for IQ. This explains why the
standard deviation for males is 12.1207 while the females is 14.2714. It is clear in the graph that
the males data is a smaller variance as the data tends to cluster closer to one spot while the
females is a bit more spread out and is less steady. The male’s graph appears to have a
2
bell-shaped curve while the female graph appears to have a more bimodal shape but both
numerically are skewed to the left as the median is greater than the mean. The mean has a bit
more of a gap as the average IQ for females measured at 105.8387 and the males measured at
110.9574.
(d)
Build a 90%, 95% and a 99% CIs for the average IQ score for all seventh-grade
girls
in this
Midwest district.
90%: (101.4883, 110.1892)
95%: (100.6039, 111.0735)
99%: (98.7899, 112.8876)
(e)
Compare and contrast the three CIs in (d)
As the number for the confidence increases in percentage the range gets larger. For example, a
90% CI has a narrower range than a 99% CI which clearly has a rider range.
(f)
Can we conclude based on the CIs that the average IQ score for all seventh-grade girls in
this Midwest district is more than 100? Justify your answer.
No, because in the 99th percentile the range starts from 98.7899 indicating that some girls from
the district got a lower score than a 100 on the IQ test.
(g)
Repeat (d) but for the seventh-grade
boys.
90%: (107.9896, 113.9253)
95%: (107.3987, 114.5162)
99%: (106.2068, 115.708)
(h)
Compare and contrast the 90% CI of the boys with that of the girls.
The boys' margin for error is smaller than the girls’. The boys’ 90% CI starts higher at 107.9896,
whereas the girls’ 90% CI begins at 101.4883. The boys’ 90% CI also ends higher at 113.9253,
compared to the girls 90% CI which ends at 110.1892. Since the boys’ data has more inputs, the
outliers affect the CI less allowing for the boy’s to have a more narrow range compared to the
females.
(i)
Estimate the proportion of students with IQ
more than
105 in two ways: a point estimate
and an interval estimate using a 90% CI.
Point estimate: 0.654
Interval Estimate: (0.56524, 0.74245)
3
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Related Questions
The IQ test scores of 74 seventh-grade girls in a midwestern school district are given.
Test Scores
115 111 97 112 104 106 113 109 113 128 128
118 113 124 127 136 106
119 97 102 110 120 103
124 126 116 127
123
115 93 123 119 110
110
107 105 105 110 90
114 106 114 100 104
89
102 91 114 114 103 105 111 108 130 120
132
111 128 118 119 86 107 100 111 103 107
112 107 103 98 96 112 112 93
To access the data, click the link for your preferred software format.
CSV Excel (xls) Excel (xlsx) JMP Mac-Text Minitab14-18 Minitab18+ PC-Text R SPSS TI CrunchIt!
These 74 girls are an SRS of all seventh-grade girls in the school district. Suppose that the standard deviation of IQ scores in
this population is known to be o = 11.
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HISTOGRAM:
3. The following is the IQ scores for 40 randomly chosen fifth graders in 2012.
108 113 126 99 117 119|102 109
129 109 13011281 13890 105
80 123 100135 140 103 133 127
139 99 114129 108 132 118 113
114 128 11098 127 120 93 85
numesical
A. What type of data is this (Categorical or Numerical)?
Use the calculator to help you draw a histogram for this IQ data. Full detail steps for using the Ti-83/84
calculator to draw a histogram given in the Chapter 11 notes.
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HISTOGRAM:
3. The following is the IQ scores for 40 randomly chosen fifth graders in 2012.
108 113 12699 117 119|102 109
129 109 130112 81 13890 105
80 123 100 135 140 103 133 127
139 99 114129|108 132118 113
114 128 110 98 127 120 93 85
A. What type of data is this (Categorical or Numerical)?
Use the calculator to help you draw a histogram for this IQ data. Full detail steps for using the Ti-83/84
calculator to draw a histogram given in the Chapter 11 notes.
B. Enter the fifth grades IQ Scores data into List 1 (L1).
C. Using STAT PLOT menu set up your calculator to draw a histogram.
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2. Solve P60 for the following list of scores resulting from statistics examination
administered to 50 students.
48
85
91
54
62
72
68
70
79
90
59
43
52
61
94
98
62
76
99
64
78
49
88
73
51
69
100
93
89
68
98
66
96
55
77
57
61
70
92
46
73
83
91
79
53
62
59
82
93
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follows:
Entrance test results of incoming senior high school students,
Batch A
80
85
75
76
81
76
75
76
76
96
85
78
73
81
89
74
74
76
86
74
90
75
88
79
86
81
90
89
88
85
95
92
92
87
87
93
94
94
75
80
78
88
87
75
76
88
80
85
75
92
Batch B
95
90
88
85
92
92
87
90
87
93
90
72
75
92
74
80
71
78
90
85
85
75
76
81
76
75
76
96
87
75
80
71
78
72
74
74
92
87
95
72
76
72
87
78
87
72
88
92
76
74
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