HP 113394 User Guide - Page 257
Statistics
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Appendix E: Formulas Used 257 Statistics Mean x = ∑x n y = ∑y n Weighted Mean xw = ∑ wx ∑w Linear Estimation n = number of data pairs yˆ = A + Bx xˆ = y − A B where B= ∑ xy − ∑ x⋅ n ∑ y ∑ x2 − (∑ x n )2 A = y − Bx r= ⎢⎣⎡∑ xy − ∑ x ⋅∑ n y ⎤ ⎥⎦ ⎡ ⎢∑ ⎢⎣ x2 − (∑ x )2 n ⋅ ⎡ ⎢∑ y 2 ⎢⎣ − (∑ y )2 n Standard Deviation sx = n∑ x 2 − (∑ x )2 n(n − 1) sy = n∑ y 2 − (∑ y )2 n(n − 1) Factorial 0! = 1 For n > 1 where n is an integer: n n!= ∏i i =1 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
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
wx
x
w
Linear Estimation
n
= number of data pairs
Bx
A
y
+
=
ˆ
B
A
y
x
−
=
ˆ
where
(
)
n
x
x
n
y
x
xy
B
2
2
∑
∑
∑
∑
∑
−
⋅
−
=
x
B
y
A
−
=
(
)
(
)
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
−
⋅
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
−
⎥
⎦
⎤
⎢
⎣
⎡
⋅
−
=
∑
∑
∑
∑
∑
∑
∑
n
y
y
n
x
x
n
y
x
xy
r
2
2
2
2
Standard Deviation
(
)
)
1
(
2
2
−
−
=
∑
∑
n
n
x
x
n
s
x
(
)
)
1
(
2
2
−
−
=
∑
∑
n
n
y
y
n
s
y
Factorial
0! = 1
For
n
> 1 where
n
is an integer:
∏
=
=
n
i
i
n
1
!