Assignment 1A
Total Marks = 70
Please show all your work. Some questions require you to use graphs, tree
diagrams, formulas, and so on that are difficult or impossible to reproduce
in word-processing programs, so you will have to print the entire
assignment and fill it out and mail it to your tutor. As an alternative to
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submit it through the appropriate drop box. If you do, make sure the
material you are submitting is legible.
Question 1
A random sample of 20 days showed the following number of cardiograms
done each day at an outpatient testing centre:
8 marks
45
25
39
5
42
48
35
12
40
16
36
27
37
30
18
22
32
54
44
29
Construct a frequency distribution for these data using a lower limit for the
first class of 5 and a class width of 10. Indicate the class limits, boundaries,
midpoints, frequencies and cumulative frequencies.
Note: As this data set does not contain fractional values, do not use the
“less than” method described on page 43 of the textbook for writing the
classes.
Introduction to Statistics
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Question 2
The amount a mother spends on prenatal care can have a long-term impact
in terms of reducing complications resulting from a baby’s low birth weight.
A random sample of 50 new mothers was asked to estimate how much they
spent on prenatal care. The results are presented in the frequency
distribution below.
2
Amount Spent on
Prenatal Care ($)
Mothers
(Number)
0–99
100–199
200–299
300–399
400–499
2
4
8
20
16
Total
50
3 marks
a.
Calculate the mean amount spent on prenatal care.
5 marks
b. Use the short-cut formula to calculate the standard deviation of
amounts spent on prenatal care.
Mathematics 215 / Assignment 1A
4 marks
c.
Construct a relative frequency polygon of amounts spent on prenatal
care. Use ruler and the graph below to construct your answer.
Note: In addition to labeling the axes correctly, indicate the relative
frequency at each point on the polygon.
4 marks
d. Construct a percentage ogive of amount spent on prenatal care. Use
ruler and the graph below to construct your answer.
Note: In addition to labeling the axes correctly, indicate the cumulative
percentage at each point on the ogive.
Introduction to Statistics
3
4
2 marks
e.
Does the frequency polygon suggest skewness in the data? If so, in
which direction?
1 mark
f.
What percentage of mothers spent less than $200 on prenatal care?
Mathematics 215 / Assignment 1A
Question 3
Random samples of households were selected from each of three regions in
a large metropolitan area. The number of households selected from each
region and the corresponding mean household incomes are provided in the
table below.
Region
A
B
C
4 marks
Households Selected
(Number)
Mean Household Income
($1,000)
75
30
20
49
80
40
What is the mean household income for all three regions combined?
Question 4
4 marks
Introduction to Statistics
A course has two quizzes of equal weight, a midterm examination that has
twice the weight of a quiz, and a final examination that has twice the weight
of the midterm exam. If a student obtains 54% and 60% on the quizzes;
55% on the midterm; and 80% on the final, what will be the student’s
weighted mean final grade?
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Question 5
5 marks
The mean amount spent by all customers at an organic food market is
estimated to be $48, and the standard deviation is estimated to be $12.
According to Chebyshev’s Theorem, at least what percentage of customers
would be expected to spend between $27 and $69?
Note: Express your answer to two decimal places of accuracy.
6
Mathematics 215 / Assignment 1A
Question 6
The following data represent ozone readings, in parts per million (ppm),
taken at 3:00 p.m. for a random sample of 18 days.
12
34
8
15
11
18
10
21
12
13
14
17
4
8
20
9
40
21
4 marks
a.
2 marks
b. In what direction, if any, are the data skewed?
2 marks
c.
5 marks
d. Calculate the standard deviation of ozone readings. Use the short-cut
formula.
Introduction to Statistics
Construct a stem-and-leaf display for these data. Place the leaves in
ascending order.
Calculate the mean ozone reading.
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8
5 marks
e.
Calculate the quartiles and the interquartile range.
5 marks
f.
Sketch a box-and-whisker plot on the graph below. Indicate any
outliers.
1 mark
g.
Within what range do the middle 50% of ozone readings fall?
Mathematics 215 / Assignment 1A
3 marks
h. Calculate the approximate value of the 70th percentile. What does this
number tell you?
3 marks
i.
Introduction to Statistics
What is the percentile rank of an ozone reading of 15? What does this
number tell you?
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