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: 32. te the (820) tedian . 5 class
e, say (821) st fre ss and
:n the "':.‘r.‘ '  . ons of
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ample he dot 5 86 EXERCISES 81. The shelf life of a highspeed photographic film is
being investigated by the manufacturer. The following
data are available. R Life Life Life Life
(days) (days) (days) (days)
126 I29 134 I41
131 132 136 145
116 128 I30 I62
125 126 I34 I29
I34 127 I20 127
I20 122 129 I33
125 l 11 I47 129
150 148 126 140
130 120 I I7 I31
I49 l 17 143 133 E Construct a histogram and comment on the properties
of the data. 82. The percentage of cotton in a material used to
manufacture men's shirts is given below. Construct a
histogram for the data. Comment on the properties of
the data. X
34.2 33.6 33.8 34.7 37.8 32.6 35.8 34.6 33.1 34.7 34.2 33.6 36.6 33.1 37.6 33.6
34.5 35.0 33.4 32.5 35.4 34.6 37.3 34.1
35.6 35.4 34.7 34.1 34.6 35.9 34.6 34.7
34.3 36.2 34.6 35.1 33.8 34.7 35.5 35.7
35.1 36.8 35.2 36.8 37.1 33.6 32.8 36.8
14.7 35.1 35.0 37.9 34.0 32.9 32.1 34.3 33.6 35.3 34.9 36.4 34.1 33.5 34.5 32.7
R 83. The following data represent the yield on 90 con
wcutive batches of ceramic substrate to which a metal
coating has been applied by a vapor»deposition
process. Construct a histogram for these data and
comment on the properties of the data. X
94.1 87.3 94.1 92.4 84.6 85.4 93.2 84.1 92.1 90.6 83.6 86.6
90.6 90.1 96.4 89.1 85.4 9 I .7
91.4 95.2 88.2 88.8 89.7 87.5
88.2 86.1 86.4 86.4 87.6 84.2
86.1 94.3 85.0 85.1 85.1 85.1
95.1 93.2 84.9 84.0 89.6 90.5
90.0 86.7 87.3 93.7 90.0 95.6
92.4 83.0 89.6 87.7 90.1 88.3
87.3 95.3 90.3 90.6 94.3 84.1 86 Exercises 193 86.6 94.1 93.1 89.4 97.3 83.7
91.2 97.8 94.6 88.6 96.8 82.9
86.1 93.1 96.3 84.1 94.4 87.3
90.4 86.4 94.7 82.6 96.1 86.4 89.1 87.6 91.1 83.1 98.0 84.5
x 84. An electronics company manufactures power
supplies for a personal computer. They produce scv
cral hundred power supplies each shift. and each unit
is subjected to a lZhour burnin test. The number of
units failing during this l2»hour test each shift is
shown below. (a) Construct a frequency distribution and histogram. (b) Find the sample mean. sample variance. and sam
ple standard deviation. 3 6 4 7 6 7
4 7 8 2 l 4
2 9 4 6 4 8
5 10 10 9 l3 7
6 l4 I4 10 I2 3
IO 13 8 7 10 6
5 10 12 9 2 7
4 9 4 l6 5 8
3 8 5 ll 7 4
ll 10 l4 I3 10 I2
9 3 .. 3 4 6
2 2 8 l3 2 l7
7 4 6 3 2 5
8 6 IO 7 6 10
4 4 8 3 4 8
2 10 6 2 10 9
6 8 4 9 8 ll
5 7 6 4 l4 7
4 I4 [5 l3 6 2
3 l3 4 3 4 8
2 12 7 4 10
8 5 5 5 8 7
10 4 3 10 7 4
9 6 2 6 9 3
ll 5 6 7 2 6 1 85. Consider the shelf life data in Exercise 8 I. Com
pute the sample mean. sample variance. and sample
standard deviation. 86. Consider the cotton percentage data in Exercise
82. Find the sample mean. sample variance. sample
standard deviation. sample ntcdian. and sample mode. 194 Chapter 8 Introduction to Statistics and Data Description 87. Consider the yield data in Exercise 83. Calculate
the sample mean, sample variance. and sample stan
dard deviation. 88. An article in Computers and Industrial Engineer
ing (2001. p. 5 1) describes the timetot‘ailure data (in
hours) for jet engines. Some of the data are repro
duced below. Failure Failure
Engine # Time Engine # Time
1 150 14 171
2 291 15 197
3 93 16 200
4 53 17 262
5 2 18 255
6 65 19 286
7 183 20 206
8 144 21 179
9 223 22 232
10 197 23 165
l l 187 24 155
12 197 25 203
13 213 (a) Construct a frequency distribution and histogram
for these data. (b) Calculate the sample mean. sample median. sam
ple variance, and sample standard deviation. 89. For the timeto—failure data in Exercise 88. sup
pose the fifth observation (2 hours) is discarded. Con
struct a frequency distribution and a histogram for the
remaining data. and calculate the sample mean. sam
ple median, sample variance. and sample standard
deviation. Compare the results with those obtained in
Exercise 88. What impact has removal of this obser
vation had on the summary statistics? 810. An article in Tecltnometrics (Vol. 19. 1977. p.
425) presents the following data on motor fuel octane
ratings of several blends of gasoline: 88.5, 87.7. 83.4. 86.7. 87.5. 91.5. 88.6. 100.3.
95.6. 93.3, 94.7. 91.1, 91.0. 94.2. 87.8. 89.9.
88.3. 87.6. 84.3. 86.7, 88.2, 90.8. 88.3. 98.8.
94.2. 92.7, 93.2. 91.0, 90.3. 93.4, 88.5. 90.1.
89.2, 88.3. 85.3. 87.9. 88.6. 90.9. 89.0, 96.1,
93.3. 91.8. 92.3. 90.4, 90.1. 93.0. 88.7, 89.9,
89.8. 89.6, 87.4. 88.4, 88.9. 91.2. 89.3, 94.4,
92.7. 91.8. 91.6. 90.4. 91.1. 92.6. 89.8, 90.6.
91.1. 90.4. 89.3. 89.7. 90.3. 91.6. 90.5. 93.7,
92.7. 92.2. 92.2. 91.2. 91.0. 92.2. 90.0. 90.7. (a) Construct a stemandleaf plot.
(b) Construct a frequency distribution and histogram. (c) Calculate the sample mean. sample variance, and
sample standard deviation. (d) Find the sample median and sample mode.
(e) Determine the skewness and kurtosis measures. 811. Consider the shelflife data in Exercise 81.
Construct a stemandleaf plot for these data. Con
struct an ordered stemandleaf plot. Use this plot to ﬁnd the 65th and 95th percentiles. 812. Consider the cotton percentage data in Exercise
82
(a) Construct a stemandleaf plot. (b) Calculate the sample mean. sample variance. and
sample standard deviation. (c) Construct an ordered stemandleaf plot. (d) Find the median and the ﬁrst and third quartiles.
(c) Find the interquartile range. (1) Determine the skewness and kurtosis measures. 813. Consider the yield data in Exercise 83. (a) Construct an ordered stemandleaf plot. (b) Find the median and the ﬁrst and third quartiles.
(c) Calculate the interquartile range. 814. Construct a box plot for the shelflife data in
Exercise 81. Interpret the data using this plot. 815. Construct a box plot for the cotton percentage
data in Exercise 82. Interpret the data using this plot. 816. Construct a box plot for the yield data in Exer
cise 83. Compare it to the histogram (Exercise 83)
and the stemandleaf plot (Exercise 813). Interpret
the data. 817. An article in the Electrical Manuﬁzcmring &
Coil Winding Conference Proceedings (1995, p. 829)
presents the results for the number of returned ship
ments for a recordofthemonth club. The company is
interested in the reason for a returned shipment. The
results are shown below. Construct a Pareto chart and
interpret the data. Reason Number of Customers
Refused 195,000
Wrong selection 50.000
Wrong answer 68.000
Canceled 5.000
Other 15.000 818. The following tal:
occurrence of ﬁnal lette
Joumal. Construct a his
any of the numerical de;
any meaning for these dz
12
1 1
ll
20
25 a
b
C
a
e
r
g 12
h
i
j
k
1
m 819. Show the following
(a) That 27:10:. —f) :1 w (b) That (x, —_r) = 820. The weight of beari
process is being investigate
provided the weights 1.18.
l.2l pounds. Find the sam
sample standard deviation. 821. The diameter of eigh
shown below. Calculate
variance. and sample stand 74.001 mm
74.005
74.003
74.001 822. The thickness of prin
important characteristic. A
the following thicknesses 63. 61. 65. 62. 61. 64. 60. at
mean, sample variance. and
What are the units of meast 823. Coding the Data. C
hoard thickness data in Exe (a) Suppose that we subtrat
number. How are the s
ance. and sample stand (b) Suppose that we multi
How are the sample ml
sample standard deviati ...
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 Fall '10
 KurtPalmer
 Standard Deviation, ore., sample mean. sample

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