# # 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.U1**Qualitative data includes all non-numerical information obtained from observations not from measurement

**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.U3**Propagation of random errors in data processing shows the impact of the uncertainties on the final result.

**11.1.U4**Experimental design and procedure usually lead to systematic errors in measurement, which cause a deviation in a particular direction

**11.1.U5**Repeat trials and measurements will reduce random errors but not systematic errors.

**11.1.AS1**Distinction between random errors and systematic errors.

**11.1.AS2**Record uncertainties in all measurements as a range (+) to an appropriate precision.

**11.1.AS3**Discussion of ways to reduce uncertainties in an experiment

**11.1.AS4**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.AS6**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.AS8**Distinction between accuracy and precision in evaluating results.

**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.G2**Note that the data value must be recorded to the same precision as the random error.

**11.1.G3**SI units should be used throughout the programme

**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.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.Uz1**Crash of the Mars Climate Orbiter spacecraft.

**11.1.Uz2**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.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.

**11.2.NoS**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.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.U3**Drawn graphs have labelled and scaled axes, and are used in quantitative measurements.

**11.2.AS1**Drawing graphs of experimental results including the correct choice of axes and scale.

**11.2.AS2**Interpretation of graphs in terms of the relationships of dependent and independent variables.

**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.AS4**Calculation of quantities from graphs by measuring slope (gradient) and intercept, including appropriate units.

**11.2.IM1**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.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.Aims1**Aim 7: Graph-plotting software may be used, including the use of spreadsheets and the derivation of best-fit lines and gradients.