Statistics; Mean; Weighted Mean; Linear Estimation - HP 12C Platinum User Manual

262 Appendix E: Formulas Used

Statistics

Mean

∑
x
x y
= =
n

Weighted Mean

∑
wx
x =
w
∑ w

Linear Estimation

n = number of data pairs
ˆ
y A Bx
= +
y A
−
ˆ
x
=
B
∑ xy
B
=
where
∑
x
A y B x
= −
⎡
∑
⎢
⎣
r
=
(
⎡
∑
2
∑ x
−
⎢
⎢
⎣

Standard Deviation

2
∑
n x
−
s
=
x
n ( n
−

Factorial

0! = 1
For n > 1 where n is an integer:
n
n ! ∏ i
=
i 1
=
∑
y
n
∑ ∑
x y
⋅
−
n
( )
2
∑
x
2
−
n
∑ ∑
x y
⋅
⎤
xy
−
⎥
n
⎦
(
)
⎡
2 ⎤
∑
x
2
∑ y
⋅ −
⎥ ⎢
n
⎥ ⎢
⎦
⎣
( )
2
∑ ∑
x n
s
=
y
) 1
)
2 ⎤
y
⎥
n
⎥
⎦
( )
2
2
∑
y y
−
n ( n ) 1
−