Math 220_ Project 3
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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.
arrow_forward
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.
arrow_forward
Do all possible ways to put meaning into the given sets of data as
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
arrow_forward
The IQ scores of 50 students are given below.
115
101
105
109
101
117
113
89
115
112
103
95
88
117
89
107
115
103
113
98
92
111
110
105
95
103
114
92
94
90
99
115
94
110
108
109
110
89
113
106
108
90
106
116
105
88
104
96
108
115
(a) Construct a grouped frequency distribution for the data. Use 85-89 for the first class and use the same width for each subsequent class.
could you help me calculate all frequency numbers and what is the correct histogram for this data?
Class
Frequency
85 - 89
-
-
-
-
-
-
arrow_forward
Cholesterol levels collected from patients two days after they had a heart attack are in the table.Cholesterol levels
arrow_forward
The IQ scores of 50 students are given below.
85
86
86 87
92
90
90
92
95
97
98
98
104
104 104
105
105
107 107 109 109 113
85
86
90
89
87
94
89
88 88 88
95 95
94 95
100 103 103 104
107
107
105
106
106
115 115 115 116
119
(a) Construct a grouped frequency distribution for the data. Use 85-89 for the first class and use the same
width for each subsequent class.
Class
Frequency
98 100
arrow_forward
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