Function
Дисперсія
Стандартне відхилення
f
=
a
A
{\displaystyle f=aA\,}
σ
f
2
=
a
2
σ
A
2
{\displaystyle \sigma _{f}^{2}=a^{2}\sigma _{A}^{2}}
σ
f
=
|
a
|
σ
A
{\displaystyle \sigma _{f}=|a|\sigma _{A}}
f
=
A
+
B
{\displaystyle f=A+B}
σ
f
2
=
σ
A
2
+
σ
B
2
+
2
σ
A
B
{\displaystyle \sigma _{f}^{2}=\sigma _{A}^{2}+\sigma _{B}^{2}+2\sigma _{AB}}
σ
f
=
σ
A
2
+
σ
B
2
+
2
σ
A
B
{\displaystyle \sigma _{f}={\sqrt {\sigma _{A}^{2}+\sigma _{B}^{2}+2\sigma _{AB}}}}
f
=
A
−
B
{\displaystyle f=A-B}
σ
f
2
=
σ
A
2
+
σ
B
2
−
2
σ
A
B
{\displaystyle \sigma _{f}^{2}=\sigma _{A}^{2}+\sigma _{B}^{2}-2\sigma _{AB}}
σ
f
=
σ
A
2
+
σ
B
2
−
2
σ
A
B
{\displaystyle \sigma _{f}={\sqrt {\sigma _{A}^{2}+\sigma _{B}^{2}-2\sigma _{AB}}}}
f
=
a
A
+
b
B
{\displaystyle f=aA+bB}
σ
f
2
=
a
2
σ
A
2
+
b
2
σ
B
2
+
2
a
b
σ
A
B
{\displaystyle \sigma _{f}^{2}=a^{2}\sigma _{A}^{2}+b^{2}\sigma _{B}^{2}+2ab\,\sigma _{AB}}
σ
f
=
a
2
σ
A
2
+
b
2
σ
B
2
+
2
a
b
σ
A
B
{\displaystyle \sigma _{f}={\sqrt {a^{2}\sigma _{A}^{2}+b^{2}\sigma _{B}^{2}+2ab\,\sigma _{AB}}}}
f
=
a
A
−
b
B
{\displaystyle f=aA-bB}
σ
f
2
=
a
2
σ
A
2
+
b
2
σ
B
2
−
2
a
b
σ
A
B
{\displaystyle \sigma _{f}^{2}=a^{2}\sigma _{A}^{2}+b^{2}\sigma _{B}^{2}-2ab\,\sigma _{AB}}
σ
f
=
a
2
σ
A
2
+
b
2
σ
B
2
−
2
a
b
σ
A
B
{\displaystyle \sigma _{f}={\sqrt {a^{2}\sigma _{A}^{2}+b^{2}\sigma _{B}^{2}-2ab\,\sigma _{AB}}}}
f
=
A
B
{\displaystyle f=AB}
σ
f
2
≈
f
2
[
(
σ
A
A
)
2
+
(
σ
B
B
)
2
+
2
σ
A
B
A
B
]
{\displaystyle \sigma _{f}^{2}\approx f^{2}\left[\left({\frac {\sigma _{A}}{A}}\right)^{2}+\left({\frac {\sigma _{B}}{B}}\right)^{2}+2{\frac {\sigma _{AB}}{AB}}\right]}
[1] [2]
σ
f
≈
|
f
|
(
σ
A
A
)
2
+
(
σ
B
B
)
2
+
2
σ
A
B
A
B
{\displaystyle \sigma _{f}\approx \left|f\right|{\sqrt {\left({\frac {\sigma _{A}}{A}}\right)^{2}+\left({\frac {\sigma _{B}}{B}}\right)^{2}+2{\frac {\sigma _{AB}}{AB}}}}}
f
=
A
B
{\displaystyle f={\frac {A}{B}}}
σ
f
2
≈
f
2
[
(
σ
A
A
)
2
+
(
σ
B
B
)
2
−
2
σ
A
B
A
B
]
{\displaystyle \sigma _{f}^{2}\approx f^{2}\left[\left({\frac {\sigma _{A}}{A}}\right)^{2}+\left({\frac {\sigma _{B}}{B}}\right)^{2}-2{\frac {\sigma _{AB}}{AB}}\right]}
[3]
σ
f
≈
|
f
|
(
σ
A
A
)
2
+
(
σ
B
B
)
2
−
2
σ
A
B
A
B
{\displaystyle \sigma _{f}\approx \left|f\right|{\sqrt {\left({\frac {\sigma _{A}}{A}}\right)^{2}+\left({\frac {\sigma _{B}}{B}}\right)^{2}-2{\frac {\sigma _{AB}}{AB}}}}}
f
=
A
A
+
B
{\displaystyle f={\frac {A}{A+B}}}
σ
f
2
≈
f
2
(
A
+
B
)
2
(
B
2
A
2
σ
A
2
+
σ
B
2
−
2
B
A
σ
A
B
)
{\displaystyle \sigma _{f}^{2}\approx {\frac {f^{2}}{\left(A+B\right)^{2}}}\left({\frac {B^{2}}{A^{2}}}\sigma _{A}^{2}+\sigma _{B}^{2}-2{\frac {B}{A}}\sigma _{AB}\right)}
σ
f
≈
|
f
A
+
B
|
B
2
A
2
σ
A
2
+
σ
B
2
−
2
B
A
σ
A
B
{\displaystyle \sigma _{f}\approx \left|{\frac {f}{A+B}}\right|{\sqrt {{\frac {B^{2}}{A^{2}}}\sigma _{A}^{2}+\sigma _{B}^{2}-2{\frac {B}{A}}\sigma _{AB}}}}
f
=
a
A
b
{\displaystyle f=aA^{b}}
σ
f
2
≈
(
a
b
A
b
−
1
σ
A
)
2
=
(
f
b
σ
A
A
)
2
{\displaystyle \sigma _{f}^{2}\approx \left({a}{b}{A}^{b-1}{\sigma _{A}}\right)^{2}=\left({\frac {{f}{b}{\sigma _{A}}}{A}}\right)^{2}}
σ
f
≈
|
a
b
A
b
−
1
σ
A
|
=
|
f
b
σ
A
A
|
{\displaystyle \sigma _{f}\approx \left|{a}{b}{A}^{b-1}{\sigma _{A}}\right|=\left|{\frac {{f}{b}{\sigma _{A}}}{A}}\right|}
f
=
a
ln
(
b
A
)
{\displaystyle f=a\ln(bA)}
σ
f
2
≈
(
a
σ
A
A
)
2
{\displaystyle \sigma _{f}^{2}\approx \left(a{\frac {\sigma _{A}}{A}}\right)^{2}}
[4]
σ
f
≈
|
a
σ
A
A
|
{\displaystyle \sigma _{f}\approx \left|a{\frac {\sigma _{A}}{A}}\right|}
f
=
a
log
10
(
b
A
)
{\displaystyle f=a\log _{10}(bA)}
σ
f
2
≈
(
a
σ
A
A
ln
(
10
)
)
2
{\displaystyle \sigma _{f}^{2}\approx \left(a{\frac {\sigma _{A}}{A\ln(10)}}\right)^{2}}
[4]
σ
f
≈
|
a
σ
A
A
ln
(
10
)
|
{\displaystyle \sigma _{f}\approx \left|a{\frac {\sigma _{A}}{A\ln(10)}}\right|}
f
=
a
e
b
A
{\displaystyle f=ae^{bA}}
σ
f
2
≈
f
2
(
b
σ
A
)
2
{\displaystyle \sigma _{f}^{2}\approx f^{2}\left(b\sigma _{A}\right)^{2}}
[5]
σ
f
≈
|
f
|
|
(
b
σ
A
)
|
{\displaystyle \sigma _{f}\approx \left|f\right|\left|\left(b\sigma _{A}\right)\right|}
f
=
a
b
A
{\displaystyle f=a^{bA}}
σ
f
2
≈
f
2
(
b
ln
(
a
)
σ
A
)
2
{\displaystyle \sigma _{f}^{2}\approx f^{2}(b\ln(a)\sigma _{A})^{2}}
σ
f
≈
|
f
|
|
b
ln
(
a
)
σ
A
|
{\displaystyle \sigma _{f}\approx \left|f\right|\left|b\ln(a)\sigma _{A}\right|}
f
=
a
sin
(
b
A
)
{\displaystyle f=a\sin(bA)}
σ
f
2
≈
[
a
b
cos
(
b
A
)
σ
A
]
2
{\displaystyle \sigma _{f}^{2}\approx \left[ab\cos(bA)\sigma _{A}\right]^{2}}
σ
f
≈
|
a
b
cos
(
b
A
)
σ
A
|
{\displaystyle \sigma _{f}\approx \left|ab\cos(bA)\sigma _{A}\right|}
f
=
a
cos
(
b
A
)
{\displaystyle f=a\cos \left(bA\right)\,}
σ
f
2
≈
[
a
b
sin
(
b
A
)
σ
A
]
2
{\displaystyle \sigma _{f}^{2}\approx \left[ab\sin(bA)\sigma _{A}\right]^{2}}
σ
f
≈
|
a
b
sin
(
b
A
)
σ
A
|
{\displaystyle \sigma _{f}\approx \left|ab\sin(bA)\sigma _{A}\right|}
f
=
a
tan
(
b
A
)
{\displaystyle f=a\tan \left(bA\right)\,}
σ
f
2
≈
[
a
b
sec
2
(
b
A
)
σ
A
]
2
{\displaystyle \sigma _{f}^{2}\approx \left[ab\sec ^{2}(bA)\sigma _{A}\right]^{2}}
σ
f
≈
|
a
b
sec
2
(
b
A
)
σ
A
|
{\displaystyle \sigma _{f}\approx \left|ab\sec ^{2}(bA)\sigma _{A}\right|}
f
=
A
B
{\displaystyle f=A^{B}}
σ
f
2
≈
f
2
[
(
B
A
σ
A
)
2
+
(
ln
(
A
)
σ
B
)
2
+
2
B
ln
(
A
)
A
σ
A
B
]
{\displaystyle \sigma _{f}^{2}\approx f^{2}\left[\left({\frac {B}{A}}\sigma _{A}\right)^{2}+\left(\ln(A)\sigma _{B}\right)^{2}+2{\frac {B\ln(A)}{A}}\sigma _{AB}\right]}
σ
f
≈
|
f
|
(
B
A
σ
A
)
2
+
(
ln
(
A
)
σ
B
)
2
+
2
B
ln
(
A
)
A
σ
A
B
{\displaystyle \sigma _{f}\approx \left|f\right|{\sqrt {\left({\frac {B}{A}}\sigma _{A}\right)^{2}+\left(\ln(A)\sigma _{B}\right)^{2}+2{\frac {B\ln(A)}{A}}\sigma _{AB}}}}
f
=
a
A
2
±
b
B
2
{\displaystyle f={\sqrt {aA^{2}\pm bB^{2}}}}
σ
f
2
≈
(
A
f
)
2
a
2
σ
A
2
+
(
B
f
)
2
b
2
σ
B
2
±
2
a
b
A
B
f
2
σ
A
B
{\displaystyle \sigma _{f}^{2}\approx \left({\frac {A}{f}}\right)^{2}a^{2}\sigma _{A}^{2}+\left({\frac {B}{f}}\right)^{2}b^{2}\sigma _{B}^{2}\pm 2ab{\frac {AB}{f^{2}}}\,\sigma _{AB}}
σ
f
≈
(
A
f
)
2
a
2
σ
A
2
+
(
B
f
)
2
b
2
σ
B
2
±
2
a
b
A
B
f
2
σ
A
B
{\displaystyle \sigma _{f}\approx {\sqrt {\left({\frac {A}{f}}\right)^{2}a^{2}\sigma _{A}^{2}+\left({\frac {B}{f}}\right)^{2}b^{2}\sigma _{B}^{2}\pm 2ab{\frac {AB}{f^{2}}}\,\sigma _{AB}}}}
![{\displaystyle \sigma _{f}^{2}\approx f^{2}\left[\left({\frac {\sigma _{A}}{A}}\right)^{2}+\left({\frac {\sigma _{B}}{B}}\right)^{2}+2{\frac {\sigma _{AB}}{AB}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9499339791864087918a8411cfc3d6d3d64adb4d)
![{\displaystyle \sigma _{f}^{2}\approx f^{2}\left[\left({\frac {\sigma _{A}}{A}}\right)^{2}+\left({\frac {\sigma _{B}}{B}}\right)^{2}-2{\frac {\sigma _{AB}}{AB}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1443509fb7b51ea477c6c24a17910bde4e81863a)
![{\displaystyle \sigma _{f}^{2}\approx \left[ab\cos(bA)\sigma _{A}\right]^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/02967f1c0ff2eb7edac9b2fad3bb020fb7fad0cf)
![{\displaystyle \sigma _{f}^{2}\approx \left[ab\sin(bA)\sigma _{A}\right]^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4f4d187dd08f03fd8b03cf3606cc9f166e5656aa)
![{\displaystyle \sigma _{f}^{2}\approx \left[ab\sec ^{2}(bA)\sigma _{A}\right]^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4308e87b0ada5699f04d64d6088e12e18fc7511f)
![{\displaystyle \sigma _{f}^{2}\approx f^{2}\left[\left({\frac {B}{A}}\sigma _{A}\right)^{2}+\left(\ln(A)\sigma _{B}\right)^{2}+2{\frac {B\ln(A)}{A}}\sigma _{AB}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/977fba6a8423710573203b5286497b3ceffeb60e)
