ch6.pdf

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CHAPTER 6
Section 6-1
6-1.
Sample average:
n
x
i
x
=
i
=
1
n
=
592.035
=
74.0044 mm
8
Sample variance:
8
x
i
=
592.035
i
=
1
8
x
i
2
=
43813.18031
i
=
1
n
n
2
x
i
x
−
2
i
i
=
1
s
=
2
i
=
1
n
(
592.035
)
2
43813.18031
−
=
8
n
−
1
8
−
1
0.0001569
=
=
0.000022414 (mm)
2
7
Sample standard deviation:
s
=
0.000022414
=
0.00473 mm
The sample standard deviation could also be found using
n
(
x
i
−
x
)
2
n
−
1
s
=
i
=
1
8
where
(
x
i
−
x
)
2
=
0.0001569
i
=
1
Dot Diagram:
.. ...:
.
-------+---------+---------+---------+---------+---------diameter
73.9920
74.0000
74.0080
74.0160
74.0240
74.0320
There appears to be a possible outlier in the data set.
6-1
6-2.
Sample average:
19
x
i
x
=
i
=
1
19
=
272.82
=
14.359 min
19
Sample variance:
19
x
i
=
272.82
i
=
1
19
x
i
2
=
10333.8964
i
=
1
n
n
2
x
i
x
−
2
i
i
=
1
s
2
=
i
=
1
n
(
272.82
)
2
10333.8964
−
=
19
19
−
1
n
−
1
6416.49
=
=
356.47 (min)
2
18
Sample standard deviation:
s
=
356.47
=
18.88 min
The sample standard deviation could also be found using
n
(
x
i
−
x
)
2
n
−
1
s
=
i
=
1
where
19
i
=
1
(
x
i
−
x
)
2
=
6416.49
6-2
6-3.
Sample average:
x
=
12
84817
=
7068.1
yards
12
Sample variance:
x
i
=
84817
i
=
1
19
x
i
2
=
600057949
i
=
1
n
n
2
x
i
x
−
2
i
i
=
1
s
2
=
i
=
1
n
(
84817
)
2
600057949
−
=
12
12
−
1
n
−
1
564324.92
=
=
51302.265
11
(
yards
)
2
Sample standard deviation:
s
=
51302.265
=
226.5
yards
The sample standard deviation could also be found using
n
i
=
1
(
x
i
−
x
)
2
n
−
1
s
=
where
12
i
=
1
(
x
i
−
x
)
2
=
564324.92
Dot Diagram: (rounding was used to create the dot diagram)
.
. : .. ..
:
:
-+---------+---------+---------+---------+---------+-----C1
6750
6900
7050
7200
7350
7500
6-3
6-4.
Sample mean:
18
x
i
x
=
18
i
=
1
18
=
2272
=
126.22 kN
18
Sample variance:
x
i
=
2272
i
=
1
18
x
i
2
=
298392
i
=
1
n
n
2
x
i
x
−
2
i
i
=
1
s
2
=
i
=
1
n
(
2272
)
2
298392
−
=
18
n
−
1
18
−
1
11615.11
=
=
683.24 (kN)
2
17
Sample standard deviation:
s
=
683.24
=
26.14 kN
The sample standard deviation could also be found using
n
i
=
1
(
x
i
−
x
)
2
n
−
1
s
=
where
18
i
=
1
(
x
i
−
x
)
2
=
11615.11
Dot Diagram:
.
:
:: .
::
.
. : .
.
+---------+---------+---------+---------+---------+-------yield
90
105
120
135
150
165
6-5.
Sample average:
6-4
x
=
8
351.8
=
43.975
8
Sample variance:
x
i
=
351.8
i
=
1
19
x
i
2
=
16528.403
i
=
1
n
n
2
x
i
x
−
2
i
i
=
1
s
2
=
i
=
1
n
(
351.8
)
2
16528.043
−
=
8
8
−
1
n
−
1
1057.998
=
=
151.143
7
Sample standard deviation:
s
=
151.143
=
12.294
The sample standard deviation could also be found using
n
i
=
1
(
x
i
−
x
)
2
n
−
1
s
=
where
8
i
=
1
(
x
i
−
x
)
2
=
1057.998
Dot Diagram:
.
. ..
.
..
.
+---------+---------+---------+---------+---------+-------
24.0
32.0
40.0
48.0
56.0
64.0
6-5

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