1
ENME392 Spring 2012
Homework 1 Solutions
Assignment:
1)
(49pts) Using the dataset of exercise 1.1 in Walpole:
3.4, 2.5, 4.8, 2.9, 3.6, 2.8, 3.3, 5.6, 3.7, 2.8, 4.4, 4.0, 5.2, 3.0, 4.8
a)
(7pts) What is the sample size?
Sample size (
n
) = 15
b)
(7pts) Calculate the sample mean
Mean (
−
x
) =
∑
=
n
i
i
n
x
1
, where x
i
is the i
th
sample and n is the number of samples.
79
.
3
15
8
.
4
0
.
3
2
.
5
0
.
4
4
.
4
8
.
2
7
.
3
6
.
5
3
.
3
8
.
2
6
.
3
9
.
2
8
.
4
5
.
2
4
.
3
=
⎟
⎠
⎞
⎜
⎝
⎛
+
+
+
+
+
+
+
+
+
+
+
+
+
+
=
−
x
c)
(7pts) Calculate the sample median
Arranging the samples in ascending order (can be performed in Excel):
2.5, 2.8, 2.8, 2.9, 3, 3.3, 3.4,
3.6
, 3.7, 4, 4.4, 4.8, 4.8, 5.2, 5.6
Since n=15, which is odd;
Median= x
(n+1)/2
= x
8
= 3.6
d)
(7pts) Calculate the sample standard deviation
Standard deviation (s)=
∑
=
−
−
⎟
⎠
⎞
⎜
⎝
⎛
−
n
i
i
n
x
x
1
2
1
, where x
i
is the i
th
sample, n=15, and
−
x
=3.79
s = 0.97
e)
(7pts) Calculate the sample variance
Variance= s
2
=0.94
f)
(7pts) Plot the data by way of a dot plot:
x-axis: 1 = 0 - 1, 2 = 1.1 - 2, 3 = 2.1 - 3 and so on.

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