# 11A: Measurements
graph LR
classDef default fill:#f9f,stroke:#333,stroke-width:4px;
NL("number line") --> SF1("1: count sig figs")
NL --> G0("Terms")
Ex("Exact numbers") --> SF1
Ex --> U2
subgraph Sig figs
SF1 --> SF2("2: combine sig figs")
click SF2 "./sigfig.html#skill-2-combining-numbers"
end
subgraph Uncertainties
U0("Notation") --> U1("Abs and Rel Uncert")
U1 --> U2("Combine uncert")
U3("Instr. uncert") --> U2
U4("Reprod. uncert") --> U2
U2 --> U5("Reporting")
SF2 --> U4
SF2 --> U1
end
subgraph Graphs
G0 --> G1("Curve fit")
G1 --> G2("Fitness of fits")
end
subgraph Evaluation
Ev0("Lit values") --> Ev1("Syst errors")
U5 --> Ev1
U5 --> Ev2("Random errors")
Ev1 --> Ev3("Goodness of results")
Ev2 --> Ev3
G2 --> Ev3
end
# Number line
# Significant figures
# Uncertainties
# Instrument & Replicate Uncertainty
# Accuracy & Precision
# Improvements
11.1.NoS
Making quantitative measurements with replicates to ensure reliabilityâprecision, accuracy, systematic, and random errors must be interpreted through replication. (3.2, 3.4)
11.1.NoS Nature of Science Making quantitative measurements with replicates to ensure reliabilityâprecision, accuracy, systematic, and random errors must be interpreted through replication. (3.2, 3.4) Precision, Reliability, Repeatability, Reproducibility, random error
11.1.U1
Qualitative data includes all non-numerical information obtained from observations not from measurement
11.1.U1 Understandings Qualitative data includes all non-numerical information obtained from observations not from measurement Qualitative results
11.1.U2
Quantitative data are obtained from measurements, and are always associated with random errors/uncertainties, determined by the apparatus, and by human limitations such as reaction times.
11.1.U2 Understandings Quantitative data are obtained from measurements, and are always associated with random errors/uncertainties, determined by the apparatus, and by human limitations such as reaction times. absolute uncertainty, Reaction time, Significant figures, Quantitative results
11.1.U3
Propagation of random errors in data processing shows the impact of the uncertainties on the final result.
11.1.U3 Understandings Propagation of random errors in data processing shows the impact of the uncertainties on the final result. Relative uncertainty
11.1.U4
Experimental design and procedure usually lead to systematic errors in measurement, which cause a deviation in a particular direction
11.1.U4 Understandings Experimental design and procedure usually lead to systematic errors in measurement, which cause a deviation in a particular direction Outlier, Percentage error, Reaction time, Systematic errors
11.1.U5
Repeat trials and measurements will reduce random errors but not systematic errors.
11.1.U5 Understandings Repeat trials and measurements will reduce random errors but not systematic errors. Percentage error, Systematic errors
11.1.AS1
Distinction between random errors and systematic errors.
11.1.AS1 Applications and skills Distinction between random errors and systematic errors. Literature value, Accuracy, Percentage error, Systematic errors
11.1.AS2
Record uncertainties in all measurements as a range (+) to an appropriate precision.
11.1.AS2 Applications and skills Record uncertainties in all measurements as a range (+) to an appropriate precision. absolute uncertainty, random error, Significant figures
11.1.AS3
Discussion of ways to reduce uncertainties in an experiment
11.1.AS3 Applications and skills Discussion of ways to reduce uncertainties in an experiment Control variable
11.1.AS4
Propagation of uncertainties in processed data, including the use of percentage uncertainties.
11.1.AS4 Applications and skills Propagation of uncertainties in processed data, including the use of percentage uncertainties.
11.1.AS5
Discussion of systematic errors in all experimental work, their impact on the results and how they can be reduced.
11.1.AS5 Applications and skills Discussion of systematic errors in all experimental work, their impact on the results and how they can be reduced. Accuracy, Best-fit line
11.1.AS6
Estimation of whether a particular source of error is likely to have a major or minor effect on the final result.
11.1.AS6 Applications and skills Estimation of whether a particular source of error is likely to have a major or minor effect on the final result.
11.1.AS7
Calculation of percentage error when the experimental result can be compared with a theoretical or accepted result.
11.1.AS7 Applications and skills Calculation of percentage error when the experimental result can be compared with a theoretical or accepted result. Literature value, Relative uncertainty, Percentage error, Systematic errors
11.1.AS8
Distinction between accuracy and precision in evaluating results.
11.1.AS8 Applications and skills Distinction between accuracy and precision in evaluating results. Accuracy, Precision, random error
11.1.G1
The number of significant figures in a result is based on the figures given in the data. When adding or subtracting, the final answer should be given to the least number of decimal places. When multiplying or dividing the final answer is given to the least number of significant figures.
11.1.G1 Guidance The number of significant figures in a result is based on the figures given in the data. When adding or subtracting, the final answer should be given to the least number of decimal places. When multiplying or dividing the final answer is given to the least number of significant figures. scientific notation
11.1.G2
Note that the data value must be recorded to the same precision as the random error.
11.1.G2 Guidance Note that the data value must be recorded to the same precision as the random error. random error
11.1.G3
SI units should be used throughout the programme
11.1.G3 Guidance SI units should be used throughout the programme SI Units
11.1.IM1
As a result of collaboration between seven international organizations, including IUPAC, the International Standards Organization (ISO) published the Guide to the Expression of Uncertainty in Measurement in 1995. This has been widely adopted in most countries and has been translated into several languages.
11.1.IM1 International-mindedness As a result of collaboration between seven international organizations, including IUPAC, the International Standards Organization (ISO) published the Guide to the Expression of Uncertainty in Measurement in 1995. This has been widely adopted in most countries and has been translated into several languages.
11.1.ToK1
Science has been described as a self-correcting and communal public endeavour. To what extent do these characteristics also apply to the other areas of knowledge?
11.1.ToK1 Theory of Knowledge Science has been described as a self-correcting and communal public endeavour. To what extent do these characteristics also apply to the other areas of knowledge?
11.1.Uz1
Crash of the Mars Climate Orbiter spacecraft.
11.1.Uz1 Utilization Crash of the Mars Climate Orbiter spacecraft.
11.1.Uz2
Original results from CERN regarding the speed of neutrinos were flawed.
11.1.Uz2 Utilization Original results from CERN regarding the speed of neutrinos were flawed.
11.1.Aims1
Aim 6: The distinction and different roles of Class A and Class B glassware could be explored
11.1.Aims1 Aims Aim 6: The distinction and different roles of Class A and Class B glassware could be explored
11.1.Aims2
Aim 8: Consider the moral obligations of scientists to communicate the full extent of their data, including experimental uncertainties. The âcold fusionâ case of Fleischmann and Pons in the 1990s is an example of when this was not fulfilled.
11.1.Aims2 Aims Aim 8: Consider the moral obligations of scientists to communicate the full extent of their data, including experimental uncertainties. The âcold fusionâ case of Fleischmann and Pons in the 1990s is an example of when this was not fulfilled.
11.2.NoS
The idea of correlationâcan be tested in experiments whose results can be displayed graphically. (2.8)
11.2.NoS Nature of Science The idea of correlationâcan be tested in experiments whose results can be displayed graphically. (2.8)
11.2.U1
Graphical techniques are an effective means of communicating the effect of an independent variable on a dependent variable, and can lead to determination of physical quantities.
11.2.U1 Understandings Graphical techniques are an effective means of communicating the effect of an independent variable on a dependent variable, and can lead to determination of physical quantities. Dependent variable, Independent variable
11.2.U2
Sketched graphs have labelled but unscaled axes, and are used to show qualitative trends, such as variables that are proportional or inversely proportional.
11.2.U2 Understandings Sketched graphs have labelled but unscaled axes, and are used to show qualitative trends, such as variables that are proportional or inversely proportional. Trend
11.2.U3
Drawn graphs have labelled and scaled axes, and are used in quantitative measurements.
11.2.U3 Understandings Drawn graphs have labelled and scaled axes, and are used in quantitative measurements. Quantitative results
11.2.AS1
Drawing graphs of experimental results including the correct choice of axes and scale.
11.2.AS1 Applications and skills Drawing graphs of experimental results including the correct choice of axes and scale. Histogram
11.2.AS2
Interpretation of graphs in terms of the relationships of dependent and independent variables.
11.2.AS2 Applications and skills Interpretation of graphs in terms of the relationships of dependent and independent variables. Histogram, Dependent variable, Independent variable
11.2.AS3
Production and interpretation of best-fit lines or curves through data points, including an assessment of when it can and cannot be considered as a linear function.
11.2.AS3 Applications and skills Production and interpretation of best-fit lines or curves through data points, including an assessment of when it can and cannot be considered as a linear function. Scatter plot
11.2.AS4
Calculation of quantities from graphs by measuring slope (gradient) and intercept, including appropriate units.
11.2.AS4 Applications and skills Calculation of quantities from graphs by measuring slope (gradient) and intercept, including appropriate units. Histogram, Intercept (of a graph)
11.2.IM1
Charts and graphs, which largely transcend language barriers, can facilitate communication between scientists worldwide.
11.2.IM1 International-mindedness Charts and graphs, which largely transcend language barriers, can facilitate communication between scientists worldwide.
11.2.ToK1
Graphs are a visual representation of data, and so use sense perception as a way of knowing. To what extent does their interpretation also rely on the other ways of knowing, such as language and reason?
11.2.ToK1 Theory of Knowledge Graphs are a visual representation of data, and so use sense perception as a way of knowing. To what extent does their interpretation also rely on the other ways of knowing, such as language and reason?
11.2.Uz1
Graphical representations of data are widely used in diverse areas such as population, finance and climate modelling. Interpretation of these statistical trends can often lead to predictions, and so underpins the setting of government policies in many areas such as health and education.
11.2.Uz1 Utilization Graphical representations of data are widely used in diverse areas such as population, finance and climate modelling. Interpretation of these statistical trends can often lead to predictions, and so underpins the setting of government policies in many areas such as health and education.
11.2.Aims1
Aim 7: Graph-plotting software may be used, including the use of spreadsheets and the derivation of best-fit lines and gradients.
11.2.Aims1 Aims Aim 7: Graph-plotting software may be used, including the use of spreadsheets and the derivation of best-fit lines and gradients. Scatter plot