MTH 220 - Evansville High School

MTH 220
Name______________________
Mid-Term Exam
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
question.
1) Statistics is the science of conducting studies to
A) monitor, study, and report on a subject.
B) collect, organize, summarize, analyze, and draw conclusions from data.
C) hypothesize, experiment, and form conclusions.
D) solve a system of equations.
1)
2) A ____________ is a characteristic or attribute of a subject that can assume different
values?
A) datum
B) variable
C) sample
D) exponent
2)
3) Classifying the fruit in a basket as apple, orange, or banana, is an example of the
___________ level of measurement?
A) nominal
B) interval
C) ordinal
D) ratio
3)
4) What level of measurement allows for the ranking of data, a precise difference between
units of measure, and also includes a true zero?
A) interval
B) ratio
C) nominal
D) ordinal
4)
5) Determine which of the following describes quantitative data.
i). the name of a chemical sample
ii). the mass of a chemical sample
iii). the color of a chemical sample
A) i and ii only
B) i, ii, and iii
C) i only
5)
6) Determine which of the following describes qualitative data.
i). the volume of a shipping container, in gallons
ii). the name of the material from which the container is made
iii). the shape of the container
A) ii and iii only
B) i, ii, and iii
C) i and ii only
D) ii only
6)
D) i and iii only
7) Determine which of the following describes nominal data.
i. My favorite days of the week are Friday, Saturday, and Tuesday.
ii. My favorite day of the week is Friday, my second-favorite is Saturday, and
third-favorite is Tuesday.
A) i only
B) both i and ii
C) neither i nor ii
D) ii only
1
7)
8) Which one of the following data are discrete?
A) the latitude and longitude of the boat's port of departure
B) the speed of the boat's propeller, in revolutions per minute
C) the number of crew members on the boat
D) the latitude and longitude of a boat at sea
8)
9) Which one of the following data are continuous?
A) the number of times the file has been downloaded
B) the number of musicians performing in the MP3 file
C) the time remaining for an MP3 music download
D) all of these represent continuous data
9)
10) Give the boundaries of the given value.
3.089
A) 2.089-4.089
C) 3.088-3.09
10)
B) 3.0889-3.0891
D) 3.0885-3.0895
11) Which of the following sample types should you always regard as unreliable?
A) voluntary response samples
B) stratified samples
C) simple random samples
D) cluster samples
11)
12) An electronics manufacturer test every 1000th cell phone to verify that it is functioning
properly. Identify the kind of sample that is being used.
A) systematic sample
B) simple random sample
C) stratified sample
D) cluster sample
12)
13) The names of all 106 students in a professor's class are written on identical slips of
paper, and the slips are placed into a large glass jar. Then, the professor selects 11
random slips from the jar. Identify the kind of sample that is being used.
A) systematic sample
B) sample of convenience
C) simple random sample
D) cluster sample
13)
14) In an advertisement for a car, a driver is shown driving expertly through a difficult road
course. At the bottom of the ad, the following is included in small print "Professional
driver on a closed course". Which of the following choices best describes this misuse
of data?
A) detached statistics
B) faulty survey questions
C) changing the subject
D) implied connections
14)
15) The lower class limit represents the smallest data value that can be included in the class.
A) False
B) True
15)
2
16) For the class 5-19, the upper class limit is
A) 19
B) 19.5
16)
C) 5
17) What are the boundaries of the class 11-18?
A) 7.5 and 21.5
C) 7
D) 4.5
17)
B) 11 and 18
D) 10.5 and 18.5
18) In an ungrouped frequency distribution of the average age of high school graduates,
what would be the boundaries for the class of graduates who were reported to be 18
years old?
A) 17.6-18.5 years old
B) 17-19 years old
C) 17.6-19.5 years old
D) 17.5-18.5 years old
18)
19) What is the midpoint of the class 6-10?
A) 8
B) 4
19)
C) 5
D) 8.5
20) Thirty students recorded the colors of their eyes, choosing from the colors brown, blue,
green, hazel, and black. This data can be appropriately summarized in a(n)
.
A) categorical frequency distribution
C) open-ended distribution
B) upper boundary
D) grouped frequency distribution
21) What are the boundaries of the class 1.87-3.43?
A) 1.865-3.435
B) 1.879-3.439
C) 1.87-3.43
21)
D) 1.82-3.48
22) The following frequency distribution presents the frequency of passenger vehicles that
pass through a certain intersection from 8:00 AM to 9:00 AM on a particular day.
Vehicle Type
Motorcycle
Sedan
SUV
Truck
20)
Frequency
11
60
80
39
What is the relative frequency of the Motorcyle category?
A) 0.058
B) 0.138
C) 11
3
D) 11%
22)
23) A recent statistics exam yielded the following 25 scores. Construct a grouped frequency
distribution with the class limits shown below.
63
55
81
77
77
86
89
82
87
79
77
63
44
74
45
51
68
80
91
87
67
96
90
59
97
Class Limits
41-50
51-60
61-70
71-80
81-90
91-100
A)
Class Limits
41-50
51-60
61-70
71-80
81-90
91-100
C)
Class Limits
41-50
51-60
61-70
71-80
81-90
91-100
Tally
Frequency
B)
Frequency
2
3
5
5
6
4
Class Limits
41-50
51-60
61-70
71-80
81-90
91-100
Frequency
2
3
4
6
7
3
Class Limits
41-50
51-60
61-70
71-80
81-90
91-100
Frequency
2
2
5
6
7
3
D)
Frequency
3
2
4
7
6
3
24) A recent statistics exam yielded the following 10 scores. Construct a frequency polygon
distribution using the class limits shown below.
80, 99, 77, 67, 93, 71, 76, 86, 79, 71
Class Limits
61-70
71-80
81-90
91-100
23)
Midpoints
Tally
Frequency
4
24)
A)
B)
C)
D)
5
25) Which of the following could be an ogive?
25)
A)
B)
C)
D)
6
26) Which of the following is a histogram?
A)
26)
B)
C)
D)
7
27) Find the class with the least number of data values.
A) 75-85
B) 55-65
C) 85-95
27)
D) 65-75
28) Graphs that show distributions using proportions instead of raw data as frequencies are
called
A) histograms.
B) relative frequency graphs.
C) ogive graphs.
D) frequency polygons.
28)
29) Classify the histogram as skewed to the left, skewed to the right, or approximately
symmetric.
29)
A) skewed to the right
B) approximately symmetric
C) skewed to the left
30) Classify the histogram as unimodal or bimodal.
A) unimodal
30)
B) bimodal
8
31) The following table presents the purchase totals (in dollars) of a random sample of
gasoline purchases at a convenience store.
Construct a relative frequency histogram using a class width of 10, and using 0 as the
lower class limit for the first class.
A)
B)
C)
9
31)
D)
32) A sample of 200 high school students were asked how many hours per week they spend
watching television.The following frequency distribution presents the results.
Construct a relative frequency polygon for the frequency distribution.
A)
10
32)
B)
C)
D)
11
33) A sample of 200 high school students were asked how many hours per week they spend
watching television.The following frequency distribution presents the results.
Construct a frequency ogive for the frequency distribution.
A)
B)
12
33)
C)
D)
34) The following pie chart presents the percentages of fish caught in each of four ratings
categories.
Match this pie chart with its corresponding Parato chart.
13
34)
A)
B)
C)
D)
14
35) Construct a dotplot for the following data.
35)
A)
B)
C)
D)
36) What is the mean of the following data set?
4, 8, 11, 12, 13
A) 9.6
B) 14.4
36)
C) 11.0
37) Find the median for the following data.
6, 7, 4, 5, 3, 7, 4
A) 4
B) 7
D) 7.0
37)
C) 3
15
D) 5
38) What is the mode of the following data set?
5, 19, 17, 13, 17, 15, 12
A) 11
B) 17
38)
C) 15
D) 13
39) The following data represent the ice cream flavor choices of 20 diners at a college
cafeteria.
Which flavor ice cream is the mode?
A) Chocolate Chip
C) Rocky Road
B) Moose Tracks
D) Vanilla
40) Find the median of the data in the following stem-and-leaf plot. The leaf represents the
ones digit.
A) 28
B) 21.2
C) 24.6
B) 12.3
C) 14
42) Determine the range for the following data set.
4, 7, 3, 16, 5, 22, 8
A) 14
B) 19
C) 4
42)
D) 3
43)
25 20 19 15 31
B) 38
C) 6.2
16
41)
D) 13.8
43) Find the sample variance for the following data set:
A) 16
40)
D) 26
41) Find the mode of the data in the following stem-and-leaf plot. The leaf represents the
ones digit.
A) 13.3
39)
D) 30.4
44) Find the sample standard deviation for the following data set:
44)
25 13 31 33 20
A) 53.4
B) 8.2
C) 66.8
D) 7.3
45) A paint manufacturer discovers that the mean volume of paint in a gallon-sized pail is 1
gallon with a standard deviation of 0.05 gallons. The paint volumes are approximately
bell-shaped. Estimate the percent of pails with volumes between 0.95 gallons and 1.05
gallons.
A) 32%
B) 95%
C) 68%
D) almost all (greater than 95%)
45)
46) Given that the mean of a set of data is 25 and the standard deviation is 3, what is the
coefficient of variation?
A) 12%
B) 0.12
C) 8.33
D) 833%
46)
47) The completion times for a certain marathon race was 3 hours with a standard deviation
of 0.5 hours. What can you determine about these data by using Chebyshev's Inequality
with K = 2?
A) No more than 75% of the completion times are between 2 hours and 4 hours.
B) At least 88.9% of the completion times are between 2 hours and 4 hours.
C) At least 75% of the completion times are between 2 hours and 4 hours.
D) At most 88.9% of the completion times are between 2 hours and 4 hours.
47)
48) For the data set below, find the first quartile.
48)
A) 75
B) 63
C) 50
D) 65
49) For the data set below, find the third quartile.
A) 57.5
B) 68
49)
C) 65
D) 75
50) For the data set below, find the IQR.
A) 74
50)
B) 13
C) 65
17
D) 9
51) If a student scored 82 points on a test where the mean score was 78.2 and the standard
deviation was 6.7. The student's z score is
.
A) 0.08
B) 11.67
C) 12.24
D) 0.57
52) Indicate which student has the higher z score.
Art Major
X = 46
X = 50.5
51)
52)
s = 5.2
Theater Major
X = 70 X = 75.1 s = 7.3
A) The art major has a higher score than the theater major.
B) The theater major has a higher score than the art major.
C) Neither student received a positive score; therefore, the higher score cannot be
determined.
D) Both students have the same score.
53) The average weekly earnings in dollars for various industries are listed below. Find the
percentile rank of 683.
755, 683, 604, 706, 649, 729, 800, 547, 821, 851
A) 45th
B) 35th
C) 40th
D) 25th
53)
54) A soft-drink bottling company fills and ships soda in plastic bottles with a target
volume of 354 milliliters. The filling machinery does not deliver a perfectly consistent
volume of liquid to each bottle, and the three quartiles for the fill volume are Q 1 = 354,
54)
Q 2 = 358, and Q 3 = 362.
Find the IQR.
A) 12
B) 4
C) 8
18
D) 9.6
55) Construct a boxplot for the data set below.
55)
A)
B)
C)
D)
56) A student received the following grades last semester. Find the student's semester grade
point average.
Course
Statistics
Physics
Sociology
Literature
Tennis
A) 1.90
Credits
4
5
3
2
1
B) 2.52
Grade/Points
A / 4.0
F / 0.0
B / 3.0
B / 3.0
D / 1.0
C) 2.13
19
D) 2.40
56)
57) A random sample of weights (in carats) of sapphires in a jeweler's collection is shown.
Find the mean of the sample.
Class Boundaries
Frequency
0.95-2.95
10
2.95-4.95
15
4.95-6.95
10
6.95-8.95
10
8.95-10.95
9
A) 5.95
B) 5.55
C) 10.80
57)
D) 5.69
58) Find the probability of getting a number greater than 4 when a die is rolled one time.
1
1
1
2
A)
B)
C)
D)
2
6
3
3
58)
59) A 12-sided die can be made from a geometric solid called a
dodecahedron. Assume that a fair dodecahedron is rolled.
59)
The sample space is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
Find P(Less than 3).
A) 2/3
B) 1/4
C) 1/6
D) 1/12
60) In a poll of 416 university students, 170 said that they were opposed to legalizing
marijuana. What is the probability that a surveyed student opposes legalization of
marijuana?
A) 0.409
B) 0.309
C) 0.591
D) 0.691
60)
61) A section of an exam contains two multiple-choice questions, each with three answer
choices (listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the
probability (as a reduced fraction) that both answers are the same ("AA", "BB" or
"CC"). [Hint: List all the outcomes of the sample space first.]
A) 1/9
B) 1/27
C) 1/3
D) 1/6
61)
62) A Karate club consists of 41 persons holding a black belt (highest rating), 59 persons
holding a brown belt (middle rating), and 73 persons holding a purple belt (lowest
rating). What is the probability that a randomly-selected club member holds a brown
belt or a purple belt?
A) 0.763
B) 0.689
C) 0.237
D) 0.311
62)
20
63) A survey asked 34,407 homeowners how many pets they owned. The results were as
followed:
Number of Pets
0
1
2
3
4 or more
Total
63)
Number of Homeowners
6120
11,915
9360
6363
649
34,407
What is the probability that a sampled homeowner has more than 1 pet?
A) 0.204
B) 0.476
C) 0.524
D) 0.178
64) A single card is drawn from a deck. Find the probability of selecting a heart or a 8 .
1
17
2
4
A)
B)
C)
D)
4
52
13
13
64)
65) A poll was taken of 13,863 working adults aged 40-70 to determine their level of
education. The participants were classified by sex and by level of education. The results
were as follows.
65)
Education Level
High School or Less
Bachelor's Degree
Master's Degree
Ph.D.
Total
Male
3043
3428
554
72
7097
Female
2133
4150
423
60
6766
Total
5176
7578
977
132
13,863
A person is selected at random. Compute the probability that the person is male or has a
Ph.D.
A) 0.516
B) 0.010
C) 0.512
D) 0.521
66) A fair coin is tossed four times. What is the probability that the sequence of tosses is
HHHT?
A) 0.0625
B) 0.25
C) 0.038
D) 0.125
66)
67) A fair die is rolled two times. What is the probability that both rolls are 1?
A) 0.167
B) 0.083
C) 0.028
D) 0.0046
67)
21
68) A certain system has two components. There are 6 different models of the first
component and 11 different models of the second. Any first component can be paired
with any second component. A salesman must select 2 of the first component and 3 of
the second to take on a sales call. How many different sets of components can the
salesman take?
A) 6P 5 11P5
B) 6C 2 11C 3
C) 6C 5 11C 5
D) 6 P 2 11P3
69) Evaluate the combination: 12C8
A) 96
69)
B) 479,001,600
C) 19,958,400
D) 495
70) A bookcase contains 2 statistics books and 5 biology books. If 2 books are chosen at
random, the chance that both are statistics books is
1
10
1
10
A)
B)
C)
D)
11
21
21
11
PROBLEM SOLVING: Construct the following and show as much detail as possible.
71) Given the following data set, find the approximate value that corresponds to the
75th percentile.
10, 44, 15, 23, 14, 18, 72, 56
71)
72) A local fundraiser wants to graphically display the contributions he has received
over the past five years. Construct a time series graph for the following data.
72)
Year
1996
1997
1998
1999
2000
68)
Contributions
$550
$700
$800
$1050
$1200
22
70)
73) Construct a frequency polygon from the following frequency distribution.
Temperature
Frequency
28.5-31.5
1
31.5-34.5
3
34.5-37.5
6
37.5-40.5
10
40.5-43.5
8
43.5-46.5
7
73)
74) The scores on a recent statistics exam are shown below. Construct a stem and leaf 74)
plot for the data.
98, 73, 64, 69, 86, 89, 77, 86, 91, 73
75) Make a boxplot for the following data set.
75)
24, 15, 34, 92, 68, 34, 78, 45, 53, 67, 83, 46
23
Answer Key
Testname: MTH 220 MIDTERM
1) B
2) B
3) A
4) B
5) D
6) A
7) A
8) C
9) C
10) D
11) A
12) A
13) C
14) D
15) B
16) A
17) D
18) D
19) A
20) A
21) A
22) A
23) B
24) D
25) C
26) D
27) C
28) B
29) C
30) B
31) D
32) A
33) D
34) C
35) C
36) A
37) D
38) B
39) D
40) D
41) C
42) B
24
Answer Key
Testname: MTH 220 MIDTERM
43) B
44) B
45) C
46) A
47) C
48) D
49) D
50) D
51) D
52) B
53) B
54) C
55) B
56) C
57) D
58) C
59) C
60) A
61) C
62) A
63) B
64) D
65) A
66) A
67) C
68) B
69) D
70) C
71) 50
72)
25
Answer Key
Testname: MTH 220 MIDTERM
73)
74) 6 4 9
7 337
8 669
9 18
75) (15, 34, 49.5, 73, 92)
26