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Appendix E: Formulas Used 257
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 257 of 275
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm
Statistics
Mean
n
x
x
∑
=
n
y
y
∑
=
Weighted Mean
∑
∑
=
w
w
x
x
w
Linear Estimation
n = number of data pairs
B
x
A
y
+
=
ˆ
B
A
y
x
−
=
ˆ
where
()
n
x
x
n
yx
xy
B
2
2
∑
∑
∑
∑
∑
−
⋅
−
=
x
B
y
A
−
=
()
()
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
−⋅
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
−
⎥
⎦
⎤
⎢
⎣
⎡
⋅
−
=
∑
∑
∑
∑
∑
∑
∑
n
y
y
n
x
x
n
yx
xy
r
2
2
2
2
Standard Deviation
()
)1(
2
2
−
−
=
∑∑
nn
xxn
s
x
()
)1(
2
2
−
−
=
∑∑
nn
yyn
s
y
Factorial
0! = 1
For n > 1 where n is an integer:
∏
=
=
n
i
in
1
!