Operation Manual

192 Appendix E: Formulas Used
Weighted Mean
Linear Estimation
n = number of data pairs
where B =
Standard Deviation
Factorial
0! = 1
For n > 1 where n is an integer:
x
w
wx
∑
w
∑
--------------=
y
ˆ
ABx+=
x
ˆ
yA–
B
------------=
xy
∑
x
∑
y
∑
⋅
n
------------------------–
x
2
∑
x
∑
()
2
2
-----------------–
-------------------------------------------
AyBx–=
r
xy
∑
x
∑
y
∑
⋅
n
------------------------–
x
2
∑
x
∑
()
2
n
-----------------– y
2
∑
y
∑
()
2
n
-----------------–⋅
-------------------------------------------------------------------------------------------=
s
x
nx
2
∑
x
∑
()
2
–
nn 1–()
---------------------------------------=
s
y
ny
2
∑
y
∑
()
2
–
nn 1–()
---------------------------------------=