ISE 261 HOMEWORK ONE
Due Date: Tuesday 2/05/2013
1. The amount of flow through a solenoid valve in an automobile’s pollution-control
system is an important characteristic. An experiment was carried out to study how flow
rate depended on four factors: ambient temperature, armature length, spring load, and
bobbin depth. Five different levels (low, mid-low, middle, mid-high, and high) of each
factor were chosen, and a single observation on flow was made for each combination of
levels. The resulting data set consisted of how many observations?
Ans:
2. The following data represent the length of life in years, measured to the nearest tenth,
of 30 similar fuel pumps:
2.0
3.0
0.3
3.3
1.3
0.4
1.5
4.0
5.9
5.8
4.7
0.7
1.0
6.0
0.2
6.0
6.6
6.5
0.2
2.3
4.5
0.3
1.5
0.5
2.5
5.0
5.6
6.0
1.2
0.2
Construct a stem-and-leaf plot for the life in years of the fuel pump using the digit to the
left of the decimal point as the stem for each observation.
Ans:
3. Compute the sample mean, sample range, and sample standard deviation for the fuel
pump data in problem #2.
Ans:
4. In a certain company, every worker receives a 10% increase in pay. How does this
affect the mean salary of this company? The standard deviation of the company
salaries?
Ans:
5. An article in the Journal of Transportation Engineering lists the following values of
fracture stress (in mega-pascals) measured for a sample of 24 mixtures of hot-mixed
asphalt (HMA).
30
75
79
80
90
105
126
138
149
179
179
190
228
232
232
236
240
242
245
247
254
274
384
470
Compute the mean, median, and the 5% and 10% trimmed means.
Ans:
6. An exoplanet is a planet beyond the Solar System, orbiting around another star. On
October 19th, 2009, European astronomers announced their discovery of 32 new planets
beyond our solar system. This detection pushes the number of known exoplanets past
400. Over 350 exoplanets are listed in the Extrasolar Planets Encyclopaedia. The vast
majority have been detected through radial velocity observations and other indirect
methods rather than actual imaging. The European astronomers discovered their planets
with the High Accuracy Radial Velocity Planet Searcher (HARPS), a spectrograph
attached to the European Southern Observatory’s 3.6 –meter telescope in Chile. The
spectrograph measures small changes in a star’s radial velocity caused by the gentle
gravitational pull from an orbiting planet. A text file on this web page lists the orbital
periods (in days) for a sample of these exoplanets. Construct a Histogram from the data
available on the text file. You may use a software package (MATLAB, Excel,
Mathematica, etc) to assist in development of your Histogram. Remember to label each
axis & title your Histogram. Also, you should offer observations of shape.
Ans:
7. Coal-fired power plants used in the electrical industry have gained public attention
because of the environmental problems associated with solid wastes generated by largescale combustion. A study was conducted to measure the EC50 (Effective
Concentration, in mg/L, that decreases 50% of the light in a luminescence bioassay) at
four different locations. The experimental data found:
Largest value = 1,350
Smallest value = 1,300
Sample mean = 1,325
s = 20.81666
Find the values of the 2-middle sample observations. (Do not use successive guessing).
Ans:
8. An article in American Antiquity discusses the strength of ancient ceramics. Several
specimens of each of three types of ceramic were tested. The loads (in kg) required to
crack the specimens are listed below. Construct comparative boxplots (placed side by
side) for the three samples and comment on the features of the three samples.
Ceramic Type
Loads (kg)
Sacaton >> 15, 30, 51, 20, 17, 19, 20, 32, 17, 15, 23, 19, 15, 18, 16, 22, 29, 15, 13, 15
Gila Plain>> 27, 18, 28, 25, 55, 21, 18, 34, 23, 30, 20, 30, 31, 25, 28, 26, 17, 19, 16, 24,
19, 9, 31, 19, 27, 20, 43, 15
Cas Grande>> 20, 16, 20, 36, 27, 35, 66, 15, 18, 24, 21, 30, 20, 24, 23, 21, 13, 21
Ans:
9. Find the Interquartile Range (IQR) for the two data sets shown below.
Find the first and third quartiles of the asphalt data in problem #5.
A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
B = {1, 2, 3, 4, 5, 6, 7, 8, 10, 12}
Ans:
10. In the following list is the number of hazardous waste sites in each of the 50 US
states. The list has been sorted into numerical order. Construct a histogram for these
data. Comment on the features.
1
2
3
4
4
5
6
8
8
9
10
10
10
11
11
11
12
12
12
12
13
13
14
15
16
17
17
18
18
19
19
20
22
23
24
25
29
30
33
37
38
39
40
55
58
77
81
96
102 107