Download Review 6 with Answers

1)
The following represents the Algebra test
scores of 20 students: 29, 31, 67, 67, 69,
70, 71, 72, 75, 77, 78, 80, 83, 85, 87, 90, 90,
91, 91, 93.
a) Create a stem-leaf.
Stem leaf
2
9
3
1
6
7 7 9
7
0 1 2 5 7 8
8
0 3 5 7
9
0 0 1 1 3
1)
The following represents the Algebra test
scores of 20 students: 29, 31, 67, 67, 69,
70, 71, 72, 75, 77, 78, 80, 83, 85, 87, 90, 90,
91, 91, 93.
b) Create a histogram.
1)
The following represents the Algebra test
scores of 20 students: 29, 31, 67, 67, 69,
70, 71, 72, 75, 77, 78, 80, 83, 85, 87, 90, 90,
91, 91, 93.
c) What is the mean, mode, and median?
Mean: 74.8
Mode: 67, 90, 91
Median: 77.5
1)
The following represents the Algebra test
scores of 20 students: 29, 31, 67, 67, 69,
70, 71, 72, 75, 77, 78, 80, 83, 85, 87, 90, 90,
91, 91, 93.
d) Create a box-plot.
29
93
69.5
77.2
88.5
1)
The following represents the Algebra test
scores of 20 students: 29, 31, 67, 67, 69,
70, 71, 72, 75, 77, 78, 80, 83, 85, 87, 90, 90,
91, 91, 93.
e) What is the interquartile range?
Q3 – Q1 = 88.5 – 69.5 = 19
f) What is the standard deviation?
Standard Deviaion = 17.17
1)
The following represents the Algebra test
scores of 20 students: 29, 31, 67, 67, 69,
70, 71, 72, 75, 77, 78, 80, 83, 85, 87, 90, 90,
91, 91, 93.
g) Suppose that a 21st score of 5 is
added. Which will likely change the
most: mean, mode, or median?
mean
Will the standard deviation increase or
decrease?
increase
1)
The following represents the Algebra test
scores of 20 students: 29, 31, 67, 67, 69,
70, 71, 72, 75, 77, 78, 80, 83, 85, 87, 90, 90,
91, 91, 93.
h) Describe the shape, center, and
spread of this data.
negatively skewed
2)
Describe the shape of the following distributions.
Use words like skewed to the left (less numbers on
the left), skewed to the right (less numbers to the
right), uniform, unimodel (one mode tower),
bimodal (two mode towers), gap, outlier,
symmetric, and bell shaped.
A
B
skewed
A: ____________
right
_______________
skewed
B: ____________
_______________
left
2)
Describe the shape of the following distributions.
Use words like skewed to the left (less numbers on
the left), skewed to the right (less numbers to the
right), uniform, unimodel (one mode tower),
bimodal (two mode towers), gap, outlier,
symmetric, and bell shaped.
C
gap
2)
Describe the shape of the following distributions.
Use words like skewed to the left (less numbers on
the left), skewed to the right (less numbers to the
right), uniform, unimodel (one mode tower),
bimodal (two mode towers), gap, outlier,
symmetric, and bell shaped.
D
bell
3)
80
Use the following box-plot to answer the
questions:
95
145
90
100
110
120
130
140
a) What is the interquartile range?
145 – 95 = 50
b) What is the maximum?
about 162
c) What is the minimum?
80
150
160
170
3)
80
Use the following box-plot to answer the
questions:
90
100
110
120
130
140
150
160
d) Draw a histogram that best models this box-plot.
170
4)
A set of data has a mean of 56.7 and a
standard deviation of 2.5. What would the
new mean and new standard deviation be if
each set of data is increased by 5?
New mean: 61.7
Standard Deviation: 2.5
5)
The following data shows the ages of
teachers: 23, 25, 25, 27, 29, 30, 31, 32, 33,
34, 36, 37, 40, 41, 42, 43, 55
a) What measure of spread is more appropriate
for this data (mean, mode, median, or standard
deviation)?
mean
b) Are there any outliers? Explain.
Q3 – Q1 = 40.5 – 28 = 12.5 = IQR
28 – 18.75 = 9.25
1.5(12.5) = 18.75
40.5 + 18.75 = 59.25
Since none of the data is less than 9.25 nor greater
than 59.25, there are NO outliers.
c) Describe the shape of this data.
skewed right (positive)
6)
A teacher interviewed 200 students and
found the following results:
Male
Female
Sophomore
.2 = 40
Junior
.1 = 20
.1 = 20
.25 = 50
Senior
.25 = 50
.1 = 20
a) How many senior males did the teacher
interview? 50
b) If the student was a sophomore, what gender was
the student more likely to be? male
c) How many more female juniors were there than
male juniors? 30
7)
The following are test scores of a Biology
test: 55, 59, 60, 61, 65, 65, 65, 70, 72, 73,
74, 76, 77, 78, 82, 88, 93, 94, 95.
a) Create a stem-leaf.
Stem leaf
5
5 9
6
0 1 5 5 5
7
0 2 3 4 6 7 8
8
2 8
9
3 4 5
7)
The following are test scores of a Biology
test: 55, 59, 60, 61, 65, 65, 65, 70, 72, 73,
74, 76, 77, 78, 82, 88, 93, 94, 95.
b) Create a histogram.
7)
The following are test scores of a Biology
test: 55, 59, 60, 61, 65, 65, 65, 70, 72, 73,
74, 76, 77, 78, 82, 88, 93, 94, 95.
c) What is the mean, mode, and median?
Mean = 73.79
Mode = 65
Median = 73
7)
The following are test scores of a Biology
test: 55, 59, 60, 61, 65, 65, 65, 70, 72, 73,
74, 76, 77, 78, 82, 88, 93, 94, 95.
d) Create a box-plot.
55
95
65
73
82
7)
The following are test scores of a Biology
test: 55, 59, 60, 61, 65, 65, 65, 70, 72, 73,
74, 76, 77, 78, 82, 88, 93, 94, 95.
e) What is the interquartile range?
IQR = 82 – 65 = 17
f) What is the standard deviation?
12.3 or 11.9
7)
The following are test scores of a Biology
test: 55, 59, 60, 61, 65, 65, 65, 70, 72, 73,
74, 76, 77, 78, 82, 88, 93, 94, 95.
g) Suppose that a 21st score of 5 is
added. Which will likely change the
most: mean, mode, or median?
mean
Will the standard deviation increase or
decrease?
increase
8)
10
Use the following box-plot to answer the
questions:
12
16
12
14
16
18
20
22
24
a) What is the interquartile range?
IQR = 16 – 12 = 4
b) What is the maximum and minimum?
Maximum = 26
Minimum = 10
26
9)
A set of data has a mean of 44.7 and a
standard deviation of 1.3. What would the
new mean and new standard deviation be if
each of the data is decreased by 3?
New mean = 41.7
Standard Deviation = 1.3
10) The following data shows household
income: 23500, 26000, 28000, 29000,
32500, 36500, 38500, 42200, 55000, 58500,
62000, 67000, 112200.
a) What measure of spread is more appropriate for this
data (mean, mode, median, or standard deviation)?
median
b) Are there any outliers? Explain.
Q3 – Q1 = 60250 – 28500 = 31750 = IQR
1.5(31750) = 47625 60250 + 31750 = 107875
112200 is an outlier.
c) Describe the shape of this data.
skewed right
d) Suppose that a millionaire is added to the data
set, which measure of spread will increase the
most? mean
11)
400 people were surveyed. Each person was asked
whether he or she prefers Drama or Comedy
movies. The results are shown in the relative
frequency table below:
Age
21-30
31-40
41
Total
Drama Comedy
Total
.25 = 100 .30 = 120 .55 = 220
.15 = 60 .06 = 24 .21 = 84
.20 = 80 .04 = 16 .24 = 96
.6 = 240 .4 = 160 1
a) How many more people prefer drama than comedy?
240 – 160 = 80
b) How many more 21-30 year olds prefer comedy than
drama? 120 – 100 = 20
c) How many total people prefer drama? 240
12)
Match the following histogram (E-H) to the correct
box-plot (A-D):
A
E
G
B
G
H
C
F
D
E
F
H
13)
The following shows the population of various
towns (in thousands)?
City
East
Population
(thousands)
30
North South
40
West
56
48
Center Wayout Salem
51
53
64
Suppose that Winstonville with a population of 26,000 is
added to the data set. Which of the following is true?
A) The mean increases.
B) The range remains the same.
C) The standard deviation increases.
D) The interquartile range increases.
14) A chair lift can hold a maximum of 40000
pounds and 200 people. A safety inspector
is determining if the chair lift is safe or not.
Which measure of central tendency of
people’s weight would be the most useful to
determine if the chair lift is safe?
A) Mean
B) Median
C) Mode
D) Standard Deviation
15)
The number of points scored by a football team in
the first eight games of the season are: 10, 14, 17,
20, 35, 35, 38, 42. What would happen to the data
distribution if the team scored 27, 27, and 28 in the
next three games.
A) The standard deviation would increase.
B) The data distribution would become more peaked
and more widely spread.
C) The data distribution would become less peaked and
less widely spread.
D)The data distribution would become more peaked
and less widely spread.
16) Which of the following is most likely to have
the highest standard deviation? To have the
lowest interquartile range?
A) The average age of 100 people surveyed at
the mall. highest standard deviation
B) The average age of 100 people living in a
retirement center.
C) The weight of 100 new-born babies.
D) The amount of TV’s that 100 households
have.
lowest interquartile range
17) Which of the following statements is true?
A) A data set with high standard deviation
means that there is low variability.
B) A data set with low standard deviation
means that the data set is spread out.
C) As the amount of data increases, the
standard deviation usually increases.
D) A data set with many outliers will have a
high standard deviation.
18) Which of the following data sets has the
highest interquartile range? Lowest
standard deviation?
A) Integers from 1-20
B) Even integers from 2-40
C) The prime numbers from 1-100
highest interquartile range
D) List of ages of 20 different teenagers
lowest standard deviation
19)
The math club has 50 members. Each member was
asked if he preferred Algebra or Geometry. The
results are shown in the relative frequency table:
Geometry
Underclassmen .36
= 18
Algebra
.28 = 14
Upperclassmen
.32 = 16
.6 = 30
Total
.04
.4
=2
= 20
Total
.64 = 32
.36 = 18
1.00 = 50
Which is true?
A) Eight more underclassmen prefer Geometry than
Algebra.
B) Thirty-six students are upperclassmen.
C) Fourteen more upperclassmen prefer Algebra than
Geometry.
D) 32 % of the students preferred Algebra.