Pre-test B
1
ANSWER KEY
MTH-4104-2 – Statistics II
A new jeans manufacturing company wishes to know which stores teenagers shop at in
their city. The company polls 100 people from all the schools in the city. Which of the
following did they use: a census, a survey or a public inquiry? Justify your answer.
A Survey.
 Only part of the population was questioned.
 It could not have been an inquiry because no experts were called upon.
/5
2
Mark wishes to know the quantity of milk adolescents from his school drink. He could ask
every single student in the school, but this is very time consuming. Instead, he decides to
ask a group of students, which he believes represent the entire student population of the
school. Name 4 characteristics Mark must consider when choosing a sample.




Sample size must be adequate.
The sample must be made up of girls and boys
The sample must be made up of adolescents of all ages
The sample must be made up of students from different grade levels in the school
/5
3
After discovering the method of transportation which is used most frequently by 1900
secondary students to get home each day, the student council conducts a survey. The
student council asks 250 students the following question:
“Which method of transportation do you use to get home each day from school?”
Determine the margin of error associated with this study.
n = 0.9604/ME2
250 = 0.9604/ME2
ME2 = 0.9604/250 = 0.0038416
ME = ±6.2%
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1
4
MTH-4104-2 – Statistics II
ANSWER KEY
Pre-test B
The following article was published in the local newspaper:
Students are Spending Enough Time at School!
That’s what 200 Quebec men and women
said in a recent survey. The survey results
are displayed in the adjacent table.
To minimize costs, the majority of the 200
people questioned resided on the island of
Montreal and were between the ages of 20
and 25.
Are Quebec students spending
enough time at school?
Women
Men
Yes
60%
80%
No
20%
10%
Undecided
20%
10%
Identify two sources of bias and explain why they are biased in the above situation.
1 – Sample size
 A sample representing the population of Quebec should be larger than 200 people.
2 – Majority of the people come from Montreal
 The people chosen for the sample, should come from all different regions of
Quebec, not just Montreal.
3 – The age group of the people questioned
 The sample should be formed from people of all different age groups.
/5
5
The table below shows the results of a survey taken by 2500 people in a large city,
seperated by region. It shows the number of people who are in favor of constructing a new
library.
Region
Central
South
East
North
West
Women
120
150
100
280
170
Men
110
150
120
120
180
Determine the interval in which the percentage of people in favor lie, ignoring the
undecided people, within a margin of error of ±4%.
1500
/2500 = 3/5 = 60% ; The margin of error is ±4%
So, between 56% and 64% of the people are in favor of constructing a new library.
/5
2
ANSWER KEY
Pre-test B
6
MTH-4104-2 – Statistics II
Below you will find two tables which display the results of a public inquiry administered
by a jeans manufacturer:
The amount of money spent
during a 12 month period on
jeans by males
Amount Spent
Number of
$
Males
[0, 25[
24
[25, 50[
52
[50, 75[
139
[75, 100[
76
[100, 125[
9
The amount of money spent
during a 12 month period on
jeans by females
Amount Spent
Number of
$
Females
[0, 25[
21
[25, 50[
19
[50, 75[
131
[75, 100[
120
[100, 125[
9
For each table, calculate the mean, median and the mode.
Mean = 18600/300 = 62
Median = li + R/f × w = 50 + (150.5 – 76)/139 × 25 = 63.399
BOYS
Mode = 62.5
Mean = 20675/300 = 68.9
Median = li + R/f × w = 50 + (150.5 – 40)/131 × 25 = 71.087
GIRLS
Mode = 62.5
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7
A boatanist notes the height, in centimeters, of 30 new flowers.
3
4
5
6
0
0
0
0
1
1
1
3
1
2
4
3
3
4
4
3
5
4
4
7
5
8 9 9 9
6 7 7 8
9
Calculate the mean, median and mode and the range of this distribution. Show all steps
in your solution.
n = 30
Mean: 1297/30 = 43.23
Mode: 39
Median: n+1/2 = 30+1/2 = 31/2 = 15th & 16th value → 43+44/2 = 87/2 = 43.5
Range: 60 – 30 = 30
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3
8
MTH-4104-2 – Statistics II
ANSWER KEY
Pre-test B
The following distribution represents the values of 21 houses on the same street:
$75 900
$78 000
$79 000
$80 000
$81 000
$82 000
$84 000
$84 000
$85 000
$88 000
$88 500
$90 000
$92 000
$94 000
$95 000
$95 000
$96 900
$97 500
$98 000
$99 000
$99 900
Which quintile rank does a house worth $84 000 belong to? Clearly show all steps in your
solution.
1
N  N
2
R5  5 
? = [13 + 0.5(2)]/21
× 5 = 3.3 = 4
Nt
4th Quintile
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9
In the adjacent table are the results obtained
by a class of students on a math exam.
Construct a box and whisker plot to represent
the dispersion of this distribution.
Results in %
42
48
52
56
60
68
72
76
84
88
92
Frequency
2
1
1
3
2
8
4
3
2
1
1
Results obtained by a class of students on a math exam
40
50
60
70
80
90
Results
Min = 42
Q1 =
Q2 = 68
Q3 =
Max = 92
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4
10
A personal trainer from a fitness centre notes the number of consecutive assisted chin ups
that each one of his clients can do. Below are the results obtained.
50, 50, 51, …, 59
60, 61, 61, …, 69
71, 72, 73, …, 78
80, 80, 80, …, 95
83 clients
90 clients
80 clients
47 clients
How many consecutive assisted chin ups did Fréderique do if her percentile rank is 58?
58 = 100 × N</300
N< = (300×58)/100 = 174
Fréderique did 72 assisted chin ups.
11
/5
MTH-4104-2 – Statistics II
ANSWER KEY
Pre-test AA
The dispersion of the results obtained by students of the same class on a math exam are
presented in a quartile diagram below.
50
58
70
85 90
State whether the following affirmations are true (T) or false (F) or impossible to tell (ND).
Justify your answer.
a) 50% of the students obtained more than 70 on their exam.
T
The median is 70, so half the group must be more than 70.
b) The class average is 70%.
ND
c) The interquartile interval is 8.
F
The interquartile interval is 85 – 58 = 27
d) There are 40 students in the class.
ND
e) A quarter of the students obtained a grade between 85 and 90.
T
Q3 = 85 → 25% are between 85 and 90
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12
Twenty students of a particular math teacher obtained the following results on their last
exam.
85
63
73
93
60
86
85
100
95
69
71
78
73
86
93
92
63
39
85
88
State whether the following affirmations are true (T) or false (F). Justify your answer.
a) The range of this distribution is 40
F
100 – 39 = 61
5
b) This distribution is bimodal
F
c) The mean is 78.85
T
d) The median is greater than the mean
T
Mode is 85
Md = 85
e) The mean is the most appropriate measure of central tendency to represent this
distribution.
F
39 is far away from the other
values. The median is a better choice.
/10
Pre-test AA
ANSWER KEY
MTH-4104-2 – Statistics II
13
Laura is participating in a math contest. She obtains the same result in the first two stages
of the contest.
1st Stage
The quartile diagram below was constructed based on the results of the participants
after one stage of competition.
80
120
168
175
200
Laura’s results are ranked in the 68th percentile.
2nd Stage
Here are the results of the 10 participants after the 2nd stage of competition.
160
160
169
170
178
180
185
188
192
195
Laura’s result is greater than the 1st quartile of this distribution.
a) What is Laura’s result?
1st stage result is between 168 and 175 because Q2 = 50% = 168 & Q3 = 75% = 175
2nd stage result is greater than 169 because Q1 = 169
So, her FINAL result must be 170, because it is both between 168 and 175 and greater than 169
b) Are the following affirmations true (T) or false (F)? Justify your answer.
1. In the 2nd stage, Laura is ranked in the 2nd quintile.
F – She is ranked in the 4th quintile
2. In the 1st stage, Laura is ranked in the 3rd quartile.
T – 68% is located in the 3rd group of 25%
6
3. The percentile rank of Laura is the same in both stages of the competition.
F – In the 1st stage, she is ranked in the 68th percentile. In the 2nd stage, she is
ranked below the 68th percentile because she obtained a score lower than the
median.
14
/10
MTH-4104-2 – Statistics II
ANSWER KEY
Pre-test AA
Below you will find the students’ grades from two Physical Science classes.
Class 1
Class 2
5
9
8
9
8
5
7
4
4
7
3
3
6
3
1
5
1
1
4
0
0
1
0
4
4
5
6
7
8
9
4
2
0
0
0
0
6
1
1
2
9
1
2
3
6
3
8
8
4
4
4
5
6
7
7
Are the following statements true (T) or false (F)?
a) The mean of Class 1 is higher than Class 2.
Mean1 = 73.625
Mean2 = 70.8
T
b) The two distributions have the same median.
Median1 = 76.5
Meadian2 = 73.5
F
c) The difference between the best grade and the worse grade of Group 1 is higher
than that of Group 2.
T
Difference1 = 94 – 45 = 49
Difference2 = 90 – 44 = 46
d) A student who obtains 76% is in the same quintile in Group 1 as in Group 2.
F
Quintile1 = 5 × (12 + 0.5)/24 = 3
Quintile2 = 5 × (8 + 0.5)/24 = 2
e) A student with a grade of 83% has a higher percentile rank in Group 1 than in
Group 2.
F
Percentile1 = (20 + 1)/24 = 83%
Percentile2 = (23+0.5)/26 = 90%
7
8
/5
Pre-test AA
15
ANSWER KEY
MTH-4104-2 – Statistics II
Associate each of the following affirmations with a matching quartile diagram AND
histogram below.
Affirmation 1: At least 25% of the students obtained 60%
3, D
Affirmation 2: About 25% of the students obtained 80% or better
4, A
Affirmation 3: The number of students who obtained 70% or better is equivalent to the
number of students who obtained between 62% and 68%
2, C
Affirmation 4: At least 50% of the students obtained a grade between 68% and 76%
1, B
8
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9
MTH-4104-2 – Statistics II
Pre-test B
FORMULAS
Sample size and margin of error
n
0.9604
ME 2
Median of a distribution grouped into classes
Md  li 
R
w
f
Mean of a distribution grouped into classes
x
 f i  mi
n
Quintile rank
R5  5 
1
N
2
Nt
N 
Percentile rank
R100  100 
1
N
2
Nt
N 
10