1.1: Interpreting Errors
- Page ID
- 29118
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)
Systematic Error
- Measurements deviate from the correct value by the same amount each time
- Errors have a pattern
Example: Time on a watch is always 5 minutes ahead of the true time
Random Error
-
Errors have no pattern
Example: Everyone’s watch shows a different time
Uncertainty in Measurement
- Number ± error
- It is the amount a number may be off from the correct value
Example: Age ±365 days
Ratio Comparison
- Shows how two numbers compare
- Reduced fraction shows comparison
Example:
\[\dfrac{65 \text{mph}}{30 \text{mph}} = \dfrac{2.2}{1} \text { (Means one speed is 2.2 times faster than the other)}\nonumber \]
Percent Error
- Percentage measurements are off from standard/correct value
- Absolute value
\[\text {Percent Error} = \dfrac{\text {Experimental/Measured Value} - \text {Accepted/Theoretical Value}}{\text {Accepted/Theoretical Value}} \times 100 \% \nonumber \]