Chapter 3 Solutions:
Section 3.1:
1.)
2.)
3.)
4.)
5.)
6.)
7.)
8.)
9.)
10.)
11.)
x = cholesterol level of a patient two days after a heart attack
270 + + 236 7110
Mean = x =
=
» 253.93
28
28
266 + 270
Median: put the data in order first. Median =
= 268
2
Mode = 288
x = length of river on the South Island of New Zealand that flow to the Tasman
Sea
76 + + 56 1489
Mean = x =
=
» 67.68 km
22
22
64 + 64
Median: put data in order first. Median =
= 64 km
2
Mode: = 56 km
x = salary of a Print-O-Matic Printing Company employee
272500 + + 66346 1698038
a.) Mean = x =
=
» $89, 370.42
19
19
Median: put data in order first. Median = $75,311
58456 + + 66346 1425538
b.) Mean = x =
=
» $79,196.56
18
18
74235 + 75311
Median: put data in order first. Median =
= $74, 773
2
c.) The mean reduced by $10,000 when the CEO’s salary was removed. The
median was not affected too much by the removal. This is because the mean is
affected by extreme values while the median is not.
d.) The CEO would prefer the mean of the entire data set, because it gives the
impression that the employees are paid more and don’t need a raise.
e.) The platen worker would want to use the median of the entire data set, because
it gives the impression that the employees are paid less and deserve a raise.
a.) Ordinal. Median and mode can be used.
b.) Ratio. Mean, median, and mode can be used.
c.) Interval. Mean, median, and mode can be used.
d.) Nominal. Mode only can be used.
Skewed right. Mean is higher than median.
x = employees score on a task
x
3.0
3.0
2.0
3.0
2.0
2.0
3.0
4.0
3.0
w
0.30
0.20
0.25
0.04
0.03
0.03
0.03
0.02
0.10
1
x*w
0.90
0.60
0.50
0.12
0.06
0.06
0.09
0.08
0.30
2.71
2.71
= 2.71
1
This employee does not need a performance enhancement plan.
Weighted average =
12.)
13.)
14.)
x = student’s grade on a task
x
w
x*w
85
0.15 12.75
76
0.15 11.40
83
0.15 12.45
74
0.10
7.40
65
0.20 13.00
79
0.25 19.75
1 76.75
76.75
Weighted average =
= 76.75
1
The student has a C in the course.
-
Section 3.2:
1.)
2.)
3.)
x = cholesterol level of a patient two days after a heart attack
Using technology,
Mean = x » 253.93
Median = 268
Range = 218
Variance = s 2 » 2276.29
Standard deviation = s » 47.71
x = length of river on the South Island of New Zealand that flow to the Tasman
Sea
x
x-x
( x - x )2
76
64
68
64
37
32
32
51
56
40
64
48
108
72
8.31818
-3.68182
0.31818
-3.68182
-30.68182
-35.68182
-35.68182
-16.68182
-11.68182
-27.68182
-3.68182
-19.68182
40.31818
4.31818
69.19215
13.55579
0.10124
13.55579
941.37397
1273.19215
1273.19215
278.28306
136.46488
766.28306
13.55579
387.37397
1625.55579
18.64669
72
4.31818
18.64669
35 -32.68182 1068.10124
80 12.31818
151.73760
56 -11.68182
136.46488
177 109.31818 11950.46488
121 53.31818 2842.82851
80 12.31818
151.73760
56 -11.68182
136.46488
1489
0 23266.77273
a.) Mean = x =
76 +
+ 56
=
1489
» 67.68 km
22
22
64 + 64
Median =
= 64 km
2
b.) Range = 177 - 32 = 145 km
23266.77273
c.) Variance = s 2 =
» 1107.9416 km 2
22 -1
Standard deviation = s = 1107.9416 » 33.29 km
4.)
5.)
x = salary of a Print-O-Matic Printing Company employee
Mean x = $89, 370.42
Median = $75,311
Range = $219,782
Variance = s 2 » 2.2986 ´109
Standard deviation = s » $47,944.13
6.)
7.)
8.)
9.)
10.)
11.)
The rivers that flow to the Pacific Ocean are longer than the ones that flow to the
Tasman Sea, since the mean length for the rivers that flow to the Pacific Ocean is
higher than the mean length of the rivers that flows to the Tasman Sea. The
lengths of the rivers that flow to the Pacific Ocean have much more variability
than the lengths of the rivers that flow to the Tasman Sea, since the standard
deviation is much higher. So there are some rivers that are very long and others
that are very short of the rivers that flow to the Pacific Ocean.
x1 = pulse rate before exercise of females who do not smoke but do drink
x2 = pulse rate after exercise of females who do not smoke but do drink
x1 » 75.45
x2 » 125.55
s1 » 11.10
s2 » 24.72
The pulse rate is higher after exercise and is less consistent after exercise.
x = time of each passage of play in rugby
a.) Mean and standard deviation
x » 21.24 sec » m
s » 14.95 sec » s
b.) At least 75% of the data is between
m ± 2s = 21.24 ± 2 (14.95 )
= ( -8.66 sec,51.14 sec )
c.) At least 88.9% of the data is between
m ± 2s = 21.24 ± 3(14.95 )
12.)
13.)
= ( -23.61 sec,66.09 sec )
x = number of deaths attributed to UV radiation in Africa in 2002
a.) -
14.)
15.)
16.)
17.)
18.)
x = time of each passage of play in rugby
Mean and standard deviation
x » 21.24 sec » m
s » 14.95 sec » s
x = 75.1 sec
75.1 - 21.24
z=
» 3.61
14.95
So 75.1 sec is unusual
x = number of deaths attributed to UV radiation in Africa in 2002
Mean and standard deviation
x » 130.98 » m
s » 205.44 » s
x = 2257
2257 -130.98
z=
» 10.35
205.44
So 2257 deaths is unusual
-
Section 3.2:
1.)
2.)
3.)
4.)
5.)
The 10th percentile means that 10% of all the test scores is less than your score.
You cannot say that you failed the test though. All of the people could have done
well on the test, but you are in the bottom 10th percent.
Your child is taller than 83% of all children of that age yet lighter than 24% of all
the children. So your child is probably a tall and thin child.
x = cholesterol level of a patient two days after a heart attack
Five-number summary:
100.0%
Maximum
75.0%
Q3
50.0%
Median
25.0%
Q1
0.0%
Minimum
360
280
224
138
48
IQR = Q3- Q1 = 280 -138 = 142
Cholesterol Two Days after a Heart Attack
6.)
7.)
x = length of river on the South Island of New Zealand that flow to the Tasman
Sea
Five-number summary:
100.0%
Maximum
177 km
75.0%
Q3
77 km
50.0%
Median
64 km
25.0%
Q1
46 km
0.0%
Minimum
32 km
IQR = Q3- Q1 = 77 - 46 = 31 km
Length of Rivers that Flow to the Tasman Sea
8.)
9.)
10.)
11.)
12.)
The pulse rate of males before exercising is much lower than for after, since the
median, Q1, Q3, and the minimum are all less than the minimum of the pulse rate
after. The maximum of the before pulse rate is much higher, which may mean
that person has an unusually high pulse rate.
Reiki may be effective at lowering pain since the minimum, Q1, median, and Q3
for after treatment are all less than the median for before treatment. However,
there is a bit of an overlap for the upper 25% of the data for after, so a complete
conclusion cannot be made.
-