LAB2Handout
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School
University of Waterloo *
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Course
292
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
Pages
6
Uploaded by ConstableCheetahMaster2428
ASSIGNMENT
QUESTION 1 – Grouped Frequency Table, Histogram, and Polygon
The following data consist of IQ scores for 50 participants
141
97
107
127
108
87
124
110
114
92
115
118
101
112
102
91
146
129
114
102
96
108
109
139
134
92
106
83
109
104
118
135
127
102
101
98
97
116
113
131
101
108
113
106
86
107
129
105
89
123
1)
Construct a grouped frequency distribution table for this data (4 marks).
X
f
cf
C%
140-149
2
50
100
130-139
4
48
96
120-129
6
44
88
110-119
10
38
76
100-109
17
28
56
90-99
7
11
22
80-89
4
4
8
C% = cf
N
× 100
C% = 4
50
× 100
C% = 0.08 × 100
C% = 8
1
2)
Construct a Frequency Histogram and a Frequency Polygon for the grouped frequency distribution with proper titles. Describe the shape of the curve (5 marks).
Both the Histogram and Polygon shapes of the curve show that they are positively (right) skewed.
2
QUESTION 2 – Real Limits and Interpolation.
1)
Using the real limits, what is the percentile rank for X = 99.5? for 109.5?
(2 marks)
For X = 99.5
C% = cf
N
× 100
C% = 11
50
× 100
C% = 22
For X = 109.5
C% = cf
N
× 100
C% = 28
50
× 100
C% = 56
2)
Using the real limits, what score is associated with the 76
th
percentile? The 88
th
percentile? (2 marks)
76
th
Percentile: 110-119 = 119.5
88
th
Percentile: 120-129 = 129.5
3)
Using interpolation, find the score associated with the 25
th
percentile. (4 marks)
Fraction = distance from the top interval/interval width
(56-25) / (56 – 22)
31/34
= 0.9118
Distance = fraction*width
0.9118 x (109.5 – 99.5)
0.9118 x 10
9.118
X = top of interval – distance
109.5 – 9.118
3
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= 100.38
4)
Using interpolation, find the percentile rank for X = 115. (4 marks)
Fraction = distance from the top interval/interval width
(119.5 – 115) / (119.5 – 109.5)
4.5/10
= 0.45
Distance = fraction*width
0.45 x (76-56)
0.45 x 20
= 9
Percentile = top % - distance
76-9
= 67
4
QUESTION 3 – Create a histogram using ggplot2 (5 marks).
Go to LEARN and navigate to CONTENT
R Activities.
Complete Activity 3 - Graphing. In addition to the document, there are two videos (Activity 3A & 3B) to help you.
1.
In R, create a vector called IQ
and fill it with the data from the 50 participants
in question 1 of this assignment.
2.
Create a data frame called Participants
and place the vector IQ
into the data frame. 3.
Use ggplot to create a histogram of the data. Use a bin width of 10, provide appropriate labels for the axes along with a title, and be sure to use red rectangles. Remove the grey background and gridlines.
Copy your histogram here:
1.
IQ <- c(141,97,107,127,108,87,124,110,114,92,115,118,101,112,102,91,146,129,1
14,102,96,108,109,139,134,92,106,83,109,104,118,135,127,102,101,98,97,1
16,113,131,101,108,113,106,86,107,129,105,89,123)
2.
Participants <- data.frame(IQ)
3.
ggplot(Participants, aes(x = IQ)) + geom_histogram(binwidth = 10, fill = "red", colour = "white") + labs(title = "IQ Scores Distribution", x = "IQ", y = "Frequency") + theme_bw() + theme(panel.grid = element_blank())
5
6
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