Question
/
Answer
Question / Answer
Question
(1)
Find the mean for the given sample data. Unless otherwise specified, round your answer
to one more decimal place
than that used for the observations.
1 8, 1 8, 1 0, 1 8, 2 0
Objectives
̅
Answer
Question
(2)
Objective : to
find the mean
of a sample
data set.
The students in Hugh Logan's math class took the Scholastic Aptitude Test. Their math
scores are shown
below. Find the mean score.
640 618 345 349 574
348 356 581 470 482
̅
(
)
Answer
Question
(3)
Last year, nine employees of an electronics company retired. Their ages at retirement
are listed below. Find
the mean retirement age.
50 62 61
52 62 58
65 52 55
̅
Answer
Question
(4)
to find the
mean of a
sample data
set.
Solve the problem. If necessary, round your answer to one more decimal place than that
used for the observations.
Let
x1= 15, x2= 9, x3= 1 4, x4= 7, and x5= 2. Compute xi
to find the
mean of a
sample data
set.
.
∑
Answer
Question
(5)
Find the median for the given sample data.
1 1, 1 3, 1 8, 21, 30, 30, 49
to find the
median of a
sample data
set. Where
the number of
data is odd
Answer
Question
(6)
The distances traveled (in miles) to 7 different swim meets are given below:
15, 19, 40, 55, 70, 72, 85
to find the
median of a
sample data
set. Where
the number of
data is odd
Answer
Question
(7)
A store manager kept track of the number of newspapers sold each week over a sevenweek
period. The results are shown below.
75, 62, 217, 159, 299, 230, 230
Objective : to
find the
median of a
sample data
set. Where
the number of
data is odd
Answer
Question
(8)
to find the
sum for a set
of data.
The number of vehicles passing through a bank driveup line during each 15minute period was
recorded. The results are shown below.
30 32 30 33
33 30 35 32
40 36 36 34
29 36 30 25
20 32 32 32
to find the
median of a
sample data
set. Where
the number of
data is even
Answer
Question
(9)
Find the mode(s) for the given sample data
-20, -2 3,-46, -2 3,-49, -23,-49
to find the
mode of a
sample data
set
Answer
Question
(10)
20, 2 1, 46, 2 1, 49, 2 1, 49
to find the
mode of a
sample data
set
Answer
Question
(11)
9 2, 5 7, 32, 5 7, 29, 9 2
to find the
median of a
sample data
set
Answer
Question
(12)
Answer
Last year, nine employees of an electronics company retired. Their ages at retirement are listed
below. Find the mode(s).
52 59 60
55 51 62
67 58 50
N0 mode
to find the
median of a
sample data
set
Question
(13)
Find the range for the given data. 13) Jeanne is currently taking college economics. The instructor
often gives quizzes. On the past five quizzes,
Jeanne got the following scores.
5 19 2 13 10
to find the
range of a
sample data
set
Answer
Question
(14)
Rich Borne is currently taking Chemistry 101. On the five laboratory assignments for the quarter,
he got
the following scores.
2640174259
to find the
range of a
sample data
set
Answer
Question
(15)
The owner of a small manufacturing plant employs six people. As part of their personnel file, she
asked each one to record to the nearest one-tenth of a mile the distance they travel one way from
home to work. The six distances are listed below.
2.3 5.5 1.1 4.3 6.4 3.5
to find the
range of a
sample data
set
Answer
Question
(16)
Answer
A class of sixth grade students kept accurate records on the amount of time they spent playing
video
games during a oneweek period. The times (in hours) are listed below.
26.7 14.7 8.3 12.9 15.1
28.7 23.0 23.6 14.3 11.0
to find the
range of a
sample data
set
Question
(17)
Find the sample standard deviation for the given data. Round your final answer to one more
decimal place than that
used for the observations. 2, 6, 15, 9, 11, 22, 1, 4, 8, 19
2
6
15
9
11
22
1
4
8
19
Answer
̅
59.29
13.69
28.09
0.49
1.69
151.29
75.69
32.49
2.89
86.49
452.1
̅
-7.7
-3.7
5.3
-0.7
1.3
12.3
-8.7
-5.7
-1.7
9.3
Sum
∑
√
̅
Question
(18)
̅
Objective : to
find the
standard
deviation of
sample
ungrouped
data.
√
15, 42, 53, 7, 9, 12, 14, 28, 47
̅
̅
15
42
53
7
9
12
Answer
̅
14
28
47
sum
10.22222
16.77778
27.77778
18.22222
16.22222
13.22222
11.22222
2.77778
21.77778
√
∑
104.493782
281.493902
771.605062
332.049302
263.160422
174.827102
125.938222
7.71606173
474.271702
2535.55556
̅
√
Objective : to
find the
standard
deviation of
sample
ungrouped
data.
Question
(19)
22, 29, 21, 24, 27, 28, 25, 36
22
29
21
24
27
28
25
36
Answer
√
̅
Question
(20)
196
205
215
185
229
278
165
̅
Answer
Question
(22)
∑
̅
Objective : to
find the
standard
deviation of
sample
ungrouped
data.
√
196, 205, 215, 185, 229, 278, 165
Answer
Question
(21)
̅
20.25
6.25
30.25
6.25
0.25
2.25
2.25
90.25
158
̅
-4.5
2.5
-5.5
-2.5
0.5
1.5
-1.5
9.5
̅
̅
-14.4286 208.184498
-5.4286 29.469698
4.5714 20.897698
-25.4286 646.613698
18.5714 344.896898
67.5714 4565.8941
-45.4286 2063.7577
7879.71429
∑
√
̅
√
Find the range for the given data.
Jeanne is currently taking college economics. The instructor often gives quizzes. On the past five
quizzes, Jeanne got the following scores.
5 19 2 13 10
The same of 13
Rich Borne is currently taking Chemistry 101. On the five laboratory assignments for the quarter,
he got
Objective : to
find the
standard
deviation of
sample
ungrouped
data.
Answer
Question
(23)
Answer
Question
(24)
the following scores.
26 40 17 42 59
The same of 14
The owner of a small manufacturing plant employs six people. As part of their personnel file, she
asked each one to record to the nearest one-tenth of a mile the distance they travel one way
from home to work. The six distances are listed below.
2.3 5.5 1.1 4.3 6.4 3.5
The same 15
The test scores of 19 students are listed below.
91 99 86 54 72
85 97 91 90 66
82 83 78 88 77
80 92 94 98
Objective : to
find the range
of a sample
data set
Answer
Question
(25)
Find the sample standard deviation for the given data. Round your final answer to one more
decimal place than that used for the observations. 2, 6, 15, 9, 11, 22, 1, 4, 8, 19
Solved in 17
Answer
Question
(26)
Answer
Question
(27)
Answer
15, 42, 53, 7, 9, 12, 14, 28, 47
Question
(28)
The manager of an electrical supply store measured the diameters of the rolls of wire in the
inventory. The diameters of the rolls (in m) are listed below.
0.299 0.173 0.227 0.177 0.634 0.621 0.127
Answer
Solved in 18
22, 29, 21, 24, 27, 28, 25, 36
Solved in 19
0.299
0.173
0.227
0.117
0.634
0.621
0.127
̅
-0.015
-0.141
-0.087
-0.197
0.32
0.307
-0.187
̅
0.000225
0.019881
0.007569
0.038809
0.1024
0.094249
0.034969
0.298102
Objective : to
find the
standard
deviation of
sample
ungrouped
data.
̅
√
∑
̅
√
Question
(29)
(i) Use the raw data to obtain the sample standard deviation of the ungrouped data. Round your
answer to
two decimal places.
(ii) Use the groupeddata formula to obtain the sample standard deviation of the grouped data in
the
frequency distribution. Round your answer to two decimal places.
(iii) Compare your answers in parts (i) and (ii).
class
200 300 400 500 600 700 800 900 -
300
400
500
600
700
800
900
1000
2
3
6
6
3
1
2
1
24
Sum
√
∑
∑
̅
230
Answer
340
320
590
780
980
600
350
500
450
460
290
470
400
490
580
570
890
680
311.6667
201.6667
221.6667
48.3333
238.3333
438.3333
58.3333
191.6667
-41.6667
-91.6667
-81.6667
251.6667
-71.6667
141.6667
-51.6667
38.3333
28.3333
348.3333
138.3333
250
350
450
550
650
750
850
950
500
1050
2700
3300
1950
750
1700
950
12900
√
̅
97136.1319
40669.4579
49136.1259
2336.10789
56802.7619
192136.082
3402.77389
36736.1239
1736.11389
8402.78389
6669.44989
63336.1279
5136.11589
20069.4539
2669.44789
1469.44189
802.775889
121336.088
19136.1019
125000
367500
1215000
1815000
1267500
562500
1445000
902500
7700000
131.6667
318.3333
-1.6667
-11.6667
148.3333
410
860
540
530
690
17336.1199
101336.09
2.77788889
136.111889
22002.7679
869933.333
Sum
37823.1884
∑
√
̅
̅
√
Objective : to find the standard deviation of sample ungrouped data. and compare it to the
standard deviation when we grouped the the data in frequency distribution.
The manager of a bank recorded the amount of time each customer spent waiting in line during
peak
business hours one Monday. The frequency distribution below summarizes the results. Find the
standard
deviation. Round your answer to one decimal place.
Question
(30)
class
04812 16 20 -
Answer
4
8
12
16
20
24
14
11
7
16
0
2
50
sum
√
∑
∑
2
6
10
14
18
22
28
66
70
224
0
44
432
√
56
396
700
3136
0
968
5256
Objective : to
find the
standard
deviation of
grouped data.
Question
(31)
210
210
210
350
350
350
350
550
550
550
740
1140
Answer
̅
-253.3333
-253.3333
-253.3333
-113.3333
-113.3333
-113.3333
-113.3333
86.6667
86.6667
86.6667
276.6667
676.6667
sum
̅
64177.7609
64177.7609
64177.7609
12844.4369
12844.4369
12844.4369
12844.4369
7511.11689
7511.11689
7511.11689
76544.4629
457877.823
800866.667
∑
√
̅
210
3
630
̅
Objective : to
find the
standard
deviation of
sample raw
data in two
ways
√
̅
̅
-253.333 64177.76
̅
192533.3
350
550
740
1140
sum
Answer
1400
1650
740
1140
5560
∑
√
̅
Question
(32)
4
3
1
1
12
-113.333
86.6667
276.6667
676.6667
̅
12844.44
7511.117
76544.46
457877.8
51377.75
22533.35
76544.46
457877.8
800866.7
√
Obtain the population standard deviation, Η, for the given data. Assume that the data represent
population data. Round your final answer to one more decimal place than that used for the
observations.
The test scores of 9 students are listed below.
704695
829546
656461
70
82
65
46
95
64
95
46
61
Sum
0.666667
12.666667
-4.333333
-23.33333
25.666667
-5.333333
25.666667
23.333333
-8.333333
∑
√
0.44444489
160.444453
18.7777749
544.444429
658.777795
28.4444409
658.777795
544.444429
69.4444389
2684
√
Objective : to find the standard deviation of population data.
Question
(33)
Obtain the population standard deviation, Η, for the given data. Assume that the data
represent
population data. Round your final answer to one more decimal place than that used for the
observations.
The weekly salaries (in dollars) of seven government workers are listed below
510 547 642 934 886 874 453
510
547
642
934
886
874
Answer
453
182.2857
145.2857
-50.2857
241.7143
193.7143
181.7143
239.2857
Sum
Objective : to
find the
standard
deviation of
population
data.
33228.0764
21107.9346
2528.65162
58425.8028
37525.23
33020.0868
57257.6462
243093.429
∑
√
√
Question
(34)
5001 10001 15001 20001 25001 -
Class
10000
15000
20000
25000
30000
12
13
14
19
22
80
7500.5
12500.5
17500.5
22500.5
27500.5
Answer
√
∑
∑
√
90006
162506.5
245007
427509.5
605011
1530040
675090003
2031412503
4287745004
9619177505
16638105006
33251530020
Objective : to
find the
standard
deviation of
grouped data.
Question
(35)
class
Answer
50 - 59
5
54.5
272.5
60 - 69
13
64.5
838.5
70 - 79
80 - 89
5
8
74.5
84.5
372.5
676
90 - 99
9
94.5
850.5
Sum
√
Question
(36)
40
∑
3010
∑
√
14851
.25
54083
.25
27751
.25
57122
80372
.25
23418
0
Objective : to
find the
standard
deviation of
grouped data.
√
∑
∑
√
Objective : to find the standard deviation of grouped data.
Answer
class
70 - 71
3
70.5
72 - 73
74 - 75
76 - 77
7
16
12
72.5
74.5
76.5
78 - 79
80 - 81
10
4
78.5
80.5
82 - 83
1
82.5
Sum
Question
(37)
53
14910.
211.5 75
36793.
507.5 75
1192
88804
918
70227
61622.
785
5
322
25921
6806.2
82.5
5
30508
4018.5 5.25
Construct a modified boxplot for the data. Identify any outliers. 37) The weights (in ounces) of 27
tomatoes are listed below.
1.7 2.0 2.2 2.2 2.4 2.5 2.5 2.5 2.6
2.6 2.6 2.7 2.7 2.7 2.8 2.8 2.8 2.9
2.9 2.9 3.0 3.0 3.1 3.1 3.3 3.6 4.2
(1.5 * .5=.75)
to construct
boxplot and
check for
outliers.
A=2.5-.75=1.75
B=4.2+.75=4.95
Answer
Question
(38)
Outlier=1.7
Construct a boxplot for the given data. Include values of the 5number summary in all boxplots. 38)
The ages of the 35 members of a track and field team are listed below. Construct a boxplot for
the data set.
15 16 18 18 18 19 20
20 20 21 21 22 22 23
23 24 24 24 25 25 26
27 27 28 29 29 30 31
31 33 34 35 39 42 48
to construct
boxplot and
check for
outliers.
Answer
Question
(39)
Determine the quartile or interquartile range as specified.
The test scores of 19 students are listed below. Find the interquartile range.
91 47 86 68 59
63 97 55 90 79
82 83 53 88 75
42 92 94 66
42, 47, 53, 55, 59, 63, 63, 66, 68, 75, 79, 82, 83, 86, 88, 90, 91, 92, 94, 97
Answer
Question
(40)
The weekly salaries (in dollars) of sixteen government workers are listed below. Find the
first quartile,
Q1
690 592 813 660
728 559 473 600
517 665 685 458
538 787 500 826
458, 473, 500, 517, 538, 559, 592, 600, 660, 665, 685, 690, 728, 787, 813, 826
to find
interquartile
range.
to find first
quartile
Answer
Question
(41)
The weekly salaries (in dollars) of sixteen government workers are listed below. Find the
third quartile,
Q3
.
492 794 545 833
506 747 611 798
690 876 450 589
709 473 636 527
450, 473, 492, 506, 527, 545, 589, 611, 636, 690, 709, 747, 794, 798, 833, 876
Answer
Question
(42)
Identify potential outliers, if any, for the given data.
The test scores of 15 students are listed below.
35 41 56 65 67
68 70 73 75 77
78 82 87 90 99
to find third
quartile
to check for
outliers.
1.5 * 65=97.5
Answer
A=65-97.5=-32.5
B=82+97.5=179.5
No outliears
Question
(43)
The weekly salaries (in dollars) of sixteen government workers are listed below.
690 586 813 646
728 554 465 621
491 677 685 360
524 787 476 986
360, 446, 465, 476, 491, 524, 554, 586, 621, 677, 685, 690, 728, 787, 813, 986
to check for
outliers.
(1.5*225.5=338.25)
Answer
A =483.5-338.25=145.25
B =709+338.25=1074.25
No outliers
Question
(44)
Answer
The weights (in pounds) of 18 randomly selected adults are given below.
131 142 186 156 178 120
127 112 174 162 167 165
132 235 9 2 161 199 150
92, 112,120, 127, 131, 132, 142, 150, 156, 161, 162, 165, 167, 174, 178, 186, 199, 235
(1.5*43=64.5)
A= 131-64.5=66.5
B=174+64.5=238.5
to check for
outliers.
No outliers
Question
(45)
Find the percentile for the data value. 45) Data set: 55 38 30 66 67 68 44;
data value: 5 5
30, 38, 44, 55, 66, 67, 68
Answer
Question
(46)
Data set: 4 6 1 4 1 0 4 1 0 1 8 1 8 2 2 6 6 1 8 1 2 2 1 8;
data value: 1 4
2, 4, 4, 6, 6, 6, 10, 10, 12, 14, 18, 18, 18, 18, 22
Answer
Question
(47)
Answer
Question
to find the
percentile for
a data value.
Find the indicated measure.
The weights (in pounds) of 30 newborn babies are listed below.Find P16.
5.5 5.7 5.8 5.9 6.1 6.1 6.4 6.4 6.5 6.6
6.7 6.7 6.7 6.9 7.0 7.0 7.0 7.1 7.2 7.2
7.4 7.5 7.7 7.7 7.8 8.0 8.1 8.1 8.3 8.7
to find the
value that
corresponds
to the 16th
percentile
Answer
Question
(48)
to find the
percentile for
a data value.
The test scores of 32 students are listed below. Find P46.
32 37 41 44 46 48 53 55
56 57 59 63 65 66 68 69
70 71 74 74 75 77 78 79
80 82 83 86 89 92 95 99
to find the
value that
corresponds
to the 16th
(49)
Question /
Answer
Question
(1)
Objectives
Question / Answer
A test score of 50.0 on a test having a mean of 69 and a
standard deviation of 10.
, and -1.9 not
unusual since this value greater than -2 and less than 2
.
Answer
Question
(2)
A weight of 110 pounds among a population having a
mean weight of 164 pounds and a standard deviation of
25.6 pounds.
, and
2.11 unusual since this value greater than 2
Answer
Question
(3)
.
Objective: Find
the z-score
corresponding to
the given value
and to determine
whether the value
is unusual
A time for the 100 meter sprint of 13.7 seconds at a school
where the mean time for the 100 meter sprint is 17.5
seconds and the standard deviation is 2.1 seconds.
, and -1.81
not unusual since this value greater than -2 and less
than 2
Answer
Objective: Find
the z-score
corresponding to
the given value
and to determine
whether the value
is unusual
Objective:
Find the zscore
correspon
ding to the
given
value and
to
determine
whether
the value
is unusual.
Question
(4)
Which is better, a score of 92 on a test with a mean of 71 and
a standard deviation of 15, or a score of 688 on a test with a
mean of 493 and a standard deviation of 150?
Objective: to
Answer
Question
(5)
Determine which
score corresponds
to the higher
relative position.
Score of 92 is better
Which is better: a score of 82 on a test with a mean of 70 and
a standard deviation of 8, or a score of 82 on a test with a
mean of 75 and a standard deviation of 4?
Objective: to
Determine which
score corresponds
to the higher
relative position.
Answer
Score of 82 in
is better
Which score has a higher relative position, a score of 38 on
Question
(6)
a test for which
test for which
= 27 and
or a score of 262.7 on a
= 200 and s = 57?
Objective: to
Answer
Question
(7)
Determine which
score corresponds
to the higher
relative position.
Both have the same relative position
Data set: 55 38
data value: 55
30
66
67
68
44;
30,38,44,55,66,67,68
Objective : to find
the percentile for
a value
Answer
.
Question
(8)
Data set: 4
12 2 18;
6
14
10
4
10
18
18
22
6
6
18
data value: 14
2 4 4 6 6 6 10 10 12 14 18 18 18 18 22
Answer
Question
(9)
Data set: 4 13 8 6
9 4 12 8 6 13;
data value: 6
4
4
13
6
4
13 2
13 15
5
2 4 4 4 4 4 5 6 6 6 8 8 9 12 13 13 13 13
13 15
Answer
Question
(10)
Data set: 122 134 126 120 128 130
122 126 136 118 122 124 119;
data value: 128
120
118
Answer
Answer
Objective : to find
the percentile for
a value
In a data set with a range of 63.5 to 102.3 and 200
observations, there are 138 observations with values less
than 89.2. Find the percentile for 89.2.
Objective : to find
the percentile for
a value
Answer
Question
(12)
Objective
: to find
the
percentile
for a
value.
125
118 118 119 120 120 122 122 122 124 125 126 126
128 130 134 136
Question
(11)
Objective:
to find the
percentile
for a
value.
Use the given sample data to find
.
49 52 52 52 74 67 55 55
49 52 52 52 55 55 67 74
Objective
: to find
the third
quartile
for a given
data.
The weights (in pounds) of 30 newborn babies are listed
Question
(13)
below. Find
.
5.5 5.7 5.8
6.7 6.7 6.7
7.4 7.5 7.7
5.9
6.9
7.7
6.1
7.0
7.8
6.1
7.0
8.0
6.4
7.0
8.1
6.4
7.1
8.1
6.5
7.2
8.3
6.6
7.2
8.7
Objective: to
find the value that
corresponds to the
16th percentile
Answer
The weights (in pounds) of 30 newborn babies are listed
Question
(14)
below. Find
.
5.5 5.7
6.7 6.7
7.4 7.5
5.8
6.7
7.7
6.0
6.9
7.7
6.1
7.0
7.8
6.1
7.0
8.0
6.3
7.0
8.1
6.4 6.5 6.6
7.1 7.2 7.2
8.1 8.3 8.7
Objective
: to find
the first
quartile
for a given
data.
Answer
Question
(15)
The test scores of 32 students are listed below. Find
32 37 41 44 46 48 53 55
56 57 59 63 65 66 68 69
70 71 74 74 75 77 78 79
80 82 83 86 89 92 95 99
1)
Answer
.
Objective: to
find the value that
corresponds to the
46th percentile
Question
(16)
The test scores of 32 students are listed below. Find
32 37 41 44 46 48 53 55
56 57 59 63 65 66 68 69
70 71 74 74 75 77 78 79
80 82 83 86 89 92 95 99
.
1)
Objective
: to find
the third
quartile
for a given
data.
Answer
Question
(17)
The test scores of 40 students are listed below. Find
30 35 43 44 47 48 54 55 56 57
59 62 63 65 66 68 69 69 71 72
72 73 74 76 77 77 78 79 80 81
81 82 83 85 89 92 93 94 97 98
, thus is
.
has the rank
34,35
Answer
Question
(18)
The test scores of 40 students are listed below. Find
30 35 43 44 47 48 54 55 56 57
59 62 63 65 66 68 69 69 71 72
72 73 74 76 77 77 78 79 80 81
81 82 83 85 89 92 93 94 97 98
.
Objective: to
find the value that
corresponds to the
56th percentile
Answer
Question
(19)
Objective
: to find
the value
that
correspon
ds to the
85th
percentile
The weights (in pounds) of 30 newborn babies are listed
below. Construct a boxplot for the data set.
5.5 5.7 5.8 5.9 6.1 6.1 6.3 6.4 6.5 6.6
6.7 6.7 6.7 6.9 7.0 7.0 7.0 7.1 7.2 7.2
7.4 7.5 7.7 7.7 7.8 8.0 8.1 8.1 8.3 8.7
Objective : to
construct boxplot
Answer
Question
(20)
The test scores of 32 students are listed below. Construct a
boxplot for the data set.
32 37 41 44 46 48 53 55
57 57 59 63 65 66 68 69
70 71 74 74 75 77 78 79
81 82 83 86 89 92 95 99
Objective
: to
construct
boxplot
Answer
Question
(21)
The test scores of 40 students are listed below. Construct a
boxplot for the data set.
25 35 43 44 47 48 54 55 56 57
59 62 63 65 66 68 69 69 71 72
72 73 74 76 77 77 78 79 80 81
81 82 83 85 89 92 93 94 97 98
Objective
: to
construct
boxplot
Answer
Question
(22)
The weekly salaries (in dollars) of 24 randomly selected
employees of a company are shown below. Construct a
boxplot for the data set.
310 320 450 460 470 500 520 540
580 600 650 700 710 840 870 900
1000 1200 1250 1300 1400 1720 2500 3700
Objective : to
construct boxplot
Answer
Question
(23)
The highest temperatures ever recorded (in °F) in 32
different U.S. states are shown below. Construct a boxplot
for the data set.
100 100 105 105 106 106 107 107
109 110 110 112 112 112 114 114
114 115 116 117 118 118 118 118
118 119 120 121 122 125 128 134
Objective
: to
construct
boxplot
Answer
Question
(24)
Describe any similarities or differences in the two
distributions represented by the following boxplots.
Assume the two boxplots have the same scale.
distribution 2
distribution 1
distribution
2
Objective
: to make
a
compariso
ns for two
boxplots
distribution 1
Answer
Its quite apparent that the distribution for 2 has
higher median than the median for the
distribution for 1 and the variation or spread
for distribution approximately the same for the
two distribution.
Describe any similarities or differences in the two
distributions represented by the following boxplots.
Assume the two boxplots have the same scale
Question
(25)
Objective : to
make a
compariso
ns for two
boxplots
Answer
Distribution 2
Distribution 1
Its quite apparent that the distribution for 1 has
higher median than the median for the
distribution for 2 the variation or spread for
distribution 2 is larger than the variation for
distribution 1
Question
(26)
Listed below are the systolic blood pressures (in mm Hg) for
a sample of men aged 20-29 and for a sample of men aged
60-69.
̅
̅
116
125
132
118
131
123
-8.1667
0.8333
7.8333
-6.1667
6.8333
-1.1667
66.6949889
0.69438889
61.3605889
38.0281889
46.6939889
1.36118889
214.833333
Sum
̅
̅
128
151
140
125
164
139
Answer
Sum
-13.1667
9.8333
-1.1667
-16.1667
22.8333
-2.1667
173.361989
96.6937889
1.36118889
261.362189
521.359589
4.69458889
1058.83333
Mean=141.166667
Standard deviation=14.5522
Men aged 20-29: 5.3%
Men aged 60-69: 10.3 %
There is substantially more variation in blood pressures of
the men aged 60-69.
Question
(27)
The customer service department of a phone company is
experimenting with two different systems. On Monday they
try the first system which is based on an automated menu
Objective: to
Find the coefficient
of variation for two
sets of data, then to
compare the
variation
system. On Tuesday they try the second system in which
each caller is immediately connected with a live agent. A
quality control manager selects a sample of seven calls each
day. He records the time for each customer to have his or
her question answered. The times (in minutes) are listed
below.
̅
̅
11.7
7.5
3.9
2.9
9.2
6.3
5.5
4.985714
0.785714
-2.814286
-3.814286
2.485714
-0.414286
-1.214286
Sum
̅
Answer
6.4
2.8
4.4
4.1
3.4
5.2
3.7
2.114286
-1.485714
0.114286
-0.185714
-0.885714
0.914286
-0.585714
Sum
Automated Menu: 45.4%
Live agent: 28.1%
24.8573441
0.61734649
7.92020569
14.5487777
6.17877409
0.17163289
1.47449049
55.7685714
̅
4.47020529
2.20734609
0.01306129
0.03448969
0.78448929
0.83591889
0.34306089
8.68857143
Objective: to
Find the coefficient
of variation for two
sets of data, then to
compare the
variation
There is substantially more variation in the times for the
automated menu system.
Objective: to Find the coefficient of variation for two sets
of data, then to compare the variation
Question
(28)
Compare the variation in heights to the variation in weights
of thirteen-year old girls. The heights (in inches) and
weights (in pounds) of nine randomly selected thirteen-year
old girls are listed below.
̅
̅
59.1
61.1
62.1
64.1
60.1
58.3
64.6
63.7
66.1
-3.0333333
-1.0333333
-0.0333333
1.9666667
-2.0333333
-3.8333333
2.4666667
1.5666667
3.9666667
Sum
9.20111091
1.06777771
0.00111111
3.86777791
4.13444431
14.6944442
6.08444461
2.45444455
15.7344447
57.24
Answer
̅
87
94
91
119
96
90
-17.11111
-10.11111
-13.11111
14.88889
-8.11111
-14.11111
̅
292.790085
102.234545
171.901205
221.679045
65.7901054
199.123425
Objective: to
Find the coefficient
of variation for two
sets of data, then to
compare the
variation
123
98
139
Sum
18.88889 356.790165
-6.11111 37.3456654
34.88889 1217.23465
2664.88889
Heights: 4.4%
Weights: 17.5%
There is substantially more variation in the weights than in
the heights of the girls.