James Bernhard
Math 160Q
September 6, 2007
Homework 1
1.9. My car is black. Since the total percentage of all colors must be 100, we subtract the
sum of the colors from 100 with Excel to find that 14.2 percent of all cars have other
colors. A bar graph of this data set produced by Excel is:
Model Year 2003 Vehicle Colors
25
15
10
5
Color
re
d
ed
iu
m
m
/d
ar
k
bl
ue
n
m
ed
iu
m
lig
ht
br
ow
gr
ay
/d
ar
k
bl
ac
k
ed
iu
m
m
te
wh
i
ve
r
0
sil
Percent
20
It is also correct to produce a pie chart if “Other” is included, since then the categories are
non-overlapping and together account for all possible cases. A pie chart of this data set
(along with the “Other” category) is:
Model Year 2003 Vehicle Colors
other
14%
silver
19%
medium red
7%
medium/dark
blue
9%
white
18%
light brown
9%
black
12%
medium/dark
gray
12%
1.25. A time series plot produced by Excel for this data set is:
Temperature (degrees F)
Mean Annual Temperatures
68
67
66
65
64
63
62
61
60
59
58
1950
Pasadena
Reading
1960
1970
1980
Year
1990
2000
1.33 A histogram produced by Excel using bin limits of multiples of 20 starting at 0 and
extending to 220 (which seem reasonable to capture the essential features of the
histogram) is as follows:
Number of wells
Devonian Richmond Dolomite Oil Recovery
20
18
16
14
12
10
8
6
4
2
0
M
e
or
0
22
0
20
0
18
0
16
0
14
0
12
0
10
80
60
40
20
Oil recovered (thousands of barrels)
The shape of this histogram is unimodal with its one major peak at about 30,000 barrels
of oil recovered. The distribution is skewed to the right. By inspection (without
computing anything), the midpoint of this distribution seems to be at about 40,000 barrels
of oil recovered. The spread of the data is from about 0 to 220,000 barrels of oil
recovered. There do not appear to be any outliers (at least none that are particularly
extreme).
1.43 (a) The five-number summary produced by Excel for this data set is: 0
(minimum), 2.17 (first quartile), 10.64 (median), 38.23 (third quartile), 88.6 (maximum).
Since the difference between the median and the first quartile is much smaller than that
from the median to the third quartile, and since the difference from the median to the
minimum is much smaller than the difference from the median to the maximum, the
distribution of this data set is skewed to the right.
(b) A histogram for the data set produced by Excel using bins of width $5 million
ranging from $0 to $90 million dollars (which seem to capture the essential features of
the histogram) is:
Number of states
Average Tornado Property Damage
25
20
15
10
5
0
M
e
or
85
75
65
55
45
35
25
15
5
Damage (millions of dollars)
The histogram does indeed reveal some outliers in the $85 million range. For the
1.5*IQR rule, we compute that the IQR is 38.23. This tells us that Q1-1.5*IQR is equal
to -55.175 and Q3+1.5*IQR is equal to 95.575. None of the data fall outside of this
range, so no outliers are predicted this way.
(c) Using Excel to compute the mean, we find that the mean is 21.95. This is
much greater than the median because the distribution is skewed so far to the right (and
also has outliers to the right but not to the left).