1.2 – Uncertainties and errors
1.2.1 Random Error and Systematic Error
This is a good question to test the concept of systematic error and random error.
Systematic error is an error due to incorrectly calibrated instruments. It cannot be reduced by repeated measurements. In the experiment, if you find that you do get a straight line, but not through the origin, that is systematic error.
Random error is an error which vary from one measurement to another. In the experiment, if you repeat measure the same quantity, but the results show a spread of values, some too large some too small, that is the random error. It is normally marked as the error bar in diagram.
Systematic error is an error due to incorrectly calibrated instruments. It cannot be reduced by repeated measurements. In the experiment, if you find that you do get a straight line, but not through the origin, that is systematic error.
Random error is an error which vary from one measurement to another. In the experiment, if you repeat measure the same quantity, but the results show a spread of values, some too large some too small, that is the random error. It is normally marked as the error bar in diagram.
1.2.2.1 Absolute Uncertainty and Percentage Uncertainty
This is a good question to test the concept of absolute uncertainty and percentage (or fractional) uncertainty.
In addition, and subtraction, the total absolute uncertainty is equal to the sum of the absolute uncertainties of each component. For example, if T=a+b-c, thenΔT= Δa + Δb + Δc
In multiplication x and division /: the total percentage uncertainties are equal to the sum of the percentage uncertainties of the components. For example, if T=ab/c, thenΔT/T= Δa/a + Δb/b+ Δc/c
In addition, and subtraction, the total absolute uncertainty is equal to the sum of the absolute uncertainties of each component. For example, if T=a+b-c, thenΔT= Δa + Δb + Δc
In multiplication x and division /: the total percentage uncertainties are equal to the sum of the percentage uncertainties of the components. For example, if T=ab/c, thenΔT/T= Δa/a + Δb/b+ Δc/c
1.2.2.2 Uncertainty Power Rule
This is a question to test the concept of fractional uncertainty of the Power.
Fractional uncertainty is the ratio of the absolute uncertainty to the mean value of a quantity. Such as Δr/r. It is used in the multiplication x and division / or Powers ^ and roots.
In Powers, the total fractional uncertainty is equal to the fractional uncertainty of the component multiplied by the absolute value of the power. For example if c=an, thenΔc/c = |n|Δa/a
Fractional uncertainty is the ratio of the absolute uncertainty to the mean value of a quantity. Such as Δr/r. It is used in the multiplication x and division / or Powers ^ and roots.
In Powers, the total fractional uncertainty is equal to the fractional uncertainty of the component multiplied by the absolute value of the power. For example if c=an, thenΔc/c = |n|Δa/a
1.2.3 Uncertainty of Gradient and Intercepts
This is a question to test the concept of Uncertainty of intercepts and gradient of the best-fit line.
The best-fit line has been drawn by eye try to minimize the distance of the points from the line. The intercept of the line is the system error of the measurement. The gradient of line is found by using two points on the line as far from each other as possible.
The idea is to draw lines of maximum and minimum gradient in such a way that they go through all the error bars.
The uncertainty in the gradient is the half of the difference of maximum and minimum gradient.
The best-fit line has been drawn by eye try to minimize the distance of the points from the line. The intercept of the line is the system error of the measurement. The gradient of line is found by using two points on the line as far from each other as possible.
The idea is to draw lines of maximum and minimum gradient in such a way that they go through all the error bars.
The uncertainty in the gradient is the half of the difference of maximum and minimum gradient.