Environmental Engineering Reference
In-Depth Information
Baecher and Christian (2003) indicate that using
Equation 3.1
corrects for a statistical
bias that results from the fact that the average is estimated from the same data that are used
to calculate the standard deviation.
For use in characterizing the uncertainties in soil and rock properties, the difference
between these definitions is not significant, and for practical purposes they can be used
interchangeably. The standard deviation of
x
has the same units as
x
.
eXaMPLe
Table 3.1
contains 25 measured values of the shear strength measured on samples of soft
saturated clay. The values of
s
u
vary from 10 to 18 kPa, and the average is 14.36 kPa. The
standard deviation, calculated using
Equation 3.1
(STDEV in Excel) is 2.14 kPa. The
standard deviation calculated using
Equation 3.2
i
s 2.13 kPa.
Table 3.1
Undrained shear strength data
(a) Sorted by test
(b) Sorted by s
u
value
(c) Sorted into bins
Test
number
Measured
s
u
(kPa)
Test
number
Measured
s
u
(kPa)
Interval or
“bin”*
No. of values
in bin
Relative
frequency
1
10
21
10
10-10.9 kPa
2
0.08
2
15
24
10
3
13
12
11
11-11.9 kPa
1
0.04
4
14
22
12
12-12.9 kPa
2
0.08
5
16
20
12
6
14
2
13
13-13.9 kPa
3
0.12
7
15
25
13
8
18
18
13
9
14
3
14
14-14.9 kPa
5
0.20
10
17
5
14
11
14
8
14
12
16
10
14
13
11
13
14
14
14
6
15
15-15.9 kPa
5
0.20
15
18
17
15
16
15
1
15
17
17
19
15
18
15
15
15
19
13
23
16
16-16.9 kPa
3
0.12
20
15
4
16
21
12
11
16
22
12
9
17
17-17.9 kPa
2
0.08
23
16
16
17
24
10
7
18
18-18.9 kPa
2
0.08
25
13
14
18
Average 14.36 kPa
Std. Dev. 2.14 kPa
COV 15%
*Data intervals, or ranges of values, have several different names. They are called “groups” or “classes” in statis-
tics, and “bins” in Microsoft Excel.
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