Chapter 2 Solutions
2.1.
The mean is
x
=
30
,
841 pounds. Only 6 of the 20 pieces of wood had breaking strengths
below the mean. The distribution is skewed to the left, which makes the mean smaller than
the “middle” of the set of numbers (the median).
2.2.
The mean is 31.25 minutes, while the median is 22.5 minutes. This is what we expect for
a right-skewed distribution like this one.
2.3.
The median is $216,200, and the mean is $265,000. The distribution of housing prices
will be right-skewed, so the mean will be higher.
2.4.
With all seasons included,
x
=
37 and
M
=
37 home runs. With the outlier removed,
x
∗
=
35 (down 2) and
M
∗
=
35
.
5 home runs (down 1.5). Means are more sensitive to
outliers, while medians are resistant to them.
2.5. (a)
The Fve-number summary (all quantities in units of pounds) is Min
=
23
,
040,
Q
1
=
30
,
315,
M
=
31
,
975,
Q
3
=
32
,
710, Max
=
33
,
650.
(b)
Note the distances between
the numbers in the Fve-number summary: In order, the gaps are 7275, 1660, 735, and 940
pounds. That the Frst two gaps are larger gives some indication of the left skew.
2.6. (a)
The stock fund varied between about
−
1
.
7% and 1.9%.
(b)
The median return for
both funds was about 0.1%.
(c)
The stock fund is much more variable—it has higher
positive returns, but also lower negative returns.
2.7.
No (barely): The
IQR
is
Q
3
−
Q
1
=
30
−
10
=
20 minutes, so we would consider any
numbers
greater than
60 minutes to be outliers.
2.8. (a)
The Fve-number summary is Min
=
5
.
7%,
Q
1
=
11
.
7%,
M
=
12
.
75%,
Q
3
=
13
.
5%,
Max
=
17
.
6%.
(b)
Yes: The
IQR
is
Q
3
−
Q
1
=
13
.
5%
−
11
.
7%
=
1
.
8%, so we
would consider to be outliers any numbers below 11
.
7%
−
2
.
7%
=
9% or above
13
.
5%
+
2
.
7%
=
16
.
2%. Along with ±lorida and Alaska, Utah is an outlier (8.5% older
residents).
2.9. (a)
x
=
32
.
4
6
=
5
.
4mgof phosphate per deciliter
of blood.
(b)
The details of the computation are shown
on the right. The standard deviation is
s
=
q
2
.
06
5
.
=
0
.
6419 mg
/
dl.
x
i
x
i
−
x
(
x
i
−
x
)
2
5.6
0.2
0.04
5.2
−
0.2
0.04
4.6
−
0.8
0.64
4.9
−
0.5
0.25
5.7
0.3
0.09
6.4
1
1
32.4
0
2.06
72