HP 12c Platinum - Statistics; Mean; Weighted Mean; Linear Estimation

262 Appendix E: Formulas Used
File name: HP 12c Pt Converted_user's guide_English_HDP0F123E02_080207 Page: 276 of 281
Printed Date: { 2007/8/2Dimension: 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
Bx
A
y +=
ˆ
B
A
y
x
−
=
ˆ
where
()
n
x
x
n
y
x
xy
B
2
2
∑
∑
∑
∑
∑
−
⋅
−
=
x
By
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
!