Page 228 - Applied statistics and probability for engineers

206 Chapter 6/Descriptive Statistics

with the following results (drag coeficients are in units of drag into clouds to promote rainfall was widely used in the 20th cen-
counts; that is, one count is equivalent to a drag coeficient of tury. Recent research has questioned its effectiveness [Journal
0.0001): 79, 100, 74, 83, 81, 85, 82, 80, and 84. Compute the of Atmospheric Research (2010, Vol. 97 (2), pp. 513– 525)]. An
sample mean, sample variance, and sample standard deviation, experiment was performed by randomly assigning 52 clouds
and construct a dot diagram. to be seeded or not. The amount of rain generated was then
6-19. The following data are the joint temperatures of the measured in acre-feet. Here are the data for the unseeded and
O-rings (°F) for each test iring or actual launch of the space seeded clouds:
shuttle rocket motor (from Presidential Commission on the Unseeded:
Space Shuttle Challenger Accident, Vol. 1, pp. 129–131): 84, 49,
61, 40, 83, 67, 45, 66, 70, 69, 80, 58, 68, 60, 67, 72, 73, 70, 57, 81.2 26.1 95.0 41.1 28.6 21.7 11.5 68.5 345.5 321.2
63, 70, 78, 52, 67, 53, 67, 75, 61, 70, 81, 76, 79, 75, 76, 58, 31. 1202.6 1.0 4.9 163.0 372.4 244.3 47.3 87.0 26.3 24.4
830.1 4.9 36.6 147.8 17.3 29.0
(a) Compute the sample mean and sample standard deviation and
construct a dot diagram of the temperature data. Seeded:
(
(b) Set aside the smallest observation 31° ) F and recompute 274.7 302.8 242.5 255.0 17.5 115.3 31.4 703.4 334.1
the quantities in part (a). Comment on your indings. How 1697.8 118.3 198.6 129.6 274.7 119.0 1656.0 7.7 430.0
“different” are the other temperatures from this last value? 40.6 92.4 200.7 32.7 4.1 978.0 489.1 2745.6
6-20. The United States has an aging infrastructure as wit- Find the sample mean, sample standard deviation, and range
nessed by several recent disasters, including the I-35 bridge of rainfall for
failure in Minnesota. Most states inspect their bridges regularly (a) All 52 clouds
and report their condition (on a scale from 1–17) to the public. (b) The unseeded clouds
Here are the condition numbers from a sample of 30 bridges (c) The seeded clouds
in New York State (https://www.dot.ny.gov/main/bridgedata):
6-23. Construct dot diagrams of the seeded and unseeded
5.08 5.44 6.66 5.07 6.80 5.43 4.83 4.00 4.41 4.38
7.00 5.72 4.53 6.43 3.97 4.19 6.26 6.72 5.26 5.48 clouds and compare their distributions in a couple of sentences.
4.95 6.33 4.93 5.61 4.66 7.00 5.57 3.42 5.18 4.54 6-24. In the 2000 Sydney Olympics, a special program initi-
ated by IOC president Juan Antonio Samaranch allowed devel-
(a) Find the sample mean and sample standard deviation of
these condition numbers. oping countries to send athletes to the Olympics without the
(b) Construct a dot diagram of the data. usual qualifying procedure. Here are the 71 times for the irst
round of the 100 meter men’s swim (in seconds).
6-21. In an attempt to measure the effects of acid rain, research-
ers measured the pH (7 is neutral and values below 7 are acidic) 60.39 49.93 53.40 51.82 50.46 51.34 50.28 50.19 52.14
of water collected from rain in Ingham County, Michigan. 50.56 52.72 50.95 49.74 49.16 52.57 52.53 52.09 52.40
49.75 54.06 53.50 50.63 51.93 51.62 52.58 53.55 51.07
5.47 5.37 5.38 4.63 5.37 3.74 3.71 4.96 4.64 5.11 49.76 49.73 50.90 59.26 49.29 52.78 112.72 49.79 49.83
5.65 5.39 4.16 5.62 4.57 4.64 5.48 4.57 4.57 4.51 52.43 51.28 52.22 49.76 49.70 52.90 50.19 54.33 62.45
4.86 4.56 4.61 4.32 3.98 5.70 4.15 3.98 5.65 3.10 51.93 52.24 52.82 50.96 48.64 51.11 50.87 52.18 54.12
5.04 4.62 4.51 4.34 4.16 4.64 5.12 3.71 4.64 5.59 50.49 49.84 52.91 52.52 50.32 51.52 52.0 52.85 52.24
(a) Find the sample mean and sample standard deviation of 49.45 51.28 49.09 58.79 49.74 49.32 50.62 49.45
these measurements. (a) Find the sample mean and sample standard deviation of
(b) Construct a dot diagram of the data. these 100 meter swim times.
6-22. Cloud seeding, a process in which chemicals such as sil- (b) Construct a dot diagram of the data.
ver iodide and frozen carbon dioxide are introduced by aircraft (c) Comment on anything unusual that you see.

6-2 Stem-and-Leaf Diagrams

The dot diagram is a useful data display for small samples up to about 20 observations. How-
ever, when the number of observations is moderately large, other graphical displays may be
more useful.
For example, consider the data in Table 6-2. These data are the compressive strengths in
pounds per square inch (psi) of 80 specimens of a new aluminum-lithium alloy undergoing
evaluation as a possible material for aircraft structural elements. The data were recorded in
the order of testing, and in this format they do not convey much information about compres-
sive strength. Questions such as “What percent of the specimens fail below 120 psi?” are not