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PSTAT 5E
Quiz Homework 2
Solutions
±
2.22
a. The scatter shown below plots the five measurements along the horizontal axis. Since there are
two “1”s, the corresponding dots are placed one above the others. The approximate center of the
data appears to be around 2.
b. The mean is the sum of the measurements divided by the number of measurements, or
2
5
10
5
3
1
1
5
0
1
=
=
+
+
+
+
=
=
∑
=
n
x
x
n
i
i
To calculate the median, the observations are first ranked from smallest to largest: 0, 1, 1, 3, 5.
Then, since n = 5 is odd, the median is the (n+1) / 2 = 3
rd
measurement, or
median
= 1. The mode
is the measurement occurring most frequently, or
mode
= 1.
c. The three measures in the part b, are located on the scatterplot. Since the median and mode are
to the left of the mean, we conclude that the measurements are skewed to the right.
±
2.26
a. There appear to be two companies with unusually high earnings per share ($1.28 and $1.64).
Hence, the data may be skewed to the right.
b
.
Mean:
5705
.
0
20
41
.
11
1
=
=
=
∑
=
n
x
x
n
i
i
Median:
To find the median, the observations are ranked from smallest to largest:
.01 .21 .29 .29 .29
.32 .33 .33 .43 .44
.54 .56 .56 .62 .72
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View Full Document.72 .84 .89 1.28 1.64
Since n = 20 is even, the median is the average of the 10
th
and 11
th
observations, or
49
.
0
2
54
.
0
44
.
0
=
+
=
median
Mode:
The mode is the observation that occurs most frequently, or
mode
= .29
c. The relative frequency histogram generated is shown Figure 2.20, with the mean, median, and
mode located along the horizontal axis. Note that the mean is larger than the median, indicating
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 Spring '08
 EduardoMontoya

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