This criterion assesses the recording, processing, and presentation of the collected data. The breakdown of the criteria is as follows.
If large amounts of raw data are collected, it is recommended that students only present a sample of the data.
SI units should be used throughout the report.
Quantitative data should also be included in the results table, depending on the protocol used.
This table does not show the uncertainties of the measurements.
| Do | Don't |
|---|---|
| Include both quantitative and qualitative raw data | Include excessive amounts of raw data when a summary will suffice |
| Present raw data to the appropriate level of precision | |
| Present raw data in an easy to read table with units and absolute uncertainties |
The use of spreadsheets might be appropriate here as they allow for easier processing of data.
Pay particular attention to the use of significant figures and decimal places in your calculations.
| Do | Don't |
|---|---|
| Present the processed data on a graph with a line of best-fit, error bars and R2 value | Forget to include units on the axis and include a title for the graph |
| Propagate the uncertainties correctly and to the correct precision | Include any measurements in error propagation which do not affect the outcome |
| Deal appropriately with outliers in the data | Forget or leave out outliers in the data |
For instance, the distance of a shot put measured using a metric tape could be expressed as: 42.50 ± 0.01 m
Another instance is the measuring of time taken to do something using a chronometer, which is expressed as:
9.58 ± 0.01 seconds
For instance, a mass recorded on a mass balance that can measure to four decimal places is more precise than one that can measure to two decimal places and therefore has a lower absolute uncertainty, as can be seen below.
2.50 ± 0.01 g
2.5000 ± 0.0001 g
Instances of systematic errors include:
Take, for instance, the data shown in the table below for three times taken using different devices to measure the time for a 100 m flat race.
| Device | Time (s) | Uncertainty (s) |
|---|---|---|
| 1 | 10.30 | ± 0.01 |
| 2 | 10.30 | ± 0.005 |
| 3 | 10.27988 | ± 1 |
For instance, measuring human heart rate by palpation for 15 seconds will have an error margin of ± 4 beats per minute.
Uncertainties of averaged values
| Trial | Change in temperature of solution ± 1.0 C |
|---|---|
| 1 | 7.5 |
| 2 | 7.0 |
| 3 | 8.0 |
The average temperature is calculated as:
$(7.5 + 7.0 + 8.0) / 3 = 7.5 \text{°C}$
The uncertainty of the averaged values is the same as the individual values, which is ± 1.0 °C. So the average temperature with the uncertainty is:
7.5 ± 1.0 °C
Note that the temperature and its uncertainty are given at the same precision, which is one decimal place.
The gradient of the best-fit line is the average of the minimum gradient and the maximum gradient.
$$m = \frac{m_{\text{maximum gradient}} + m_{\text{minimum gradient}}}{2}$$
The uncertainty of the final gradient is calculated as follows:
$$\Delta m = \frac{m_{\text{maximum gradient}} - m_{\text{minimum gradient}}}{2}$$
R² – the coefficient of determination
Consider the two graphs shown and their R² values.
The graph on the left, with an R² of 1.0, indicates that all (100%) of the variation in the dependent variable is explained by the independent variable. The linear model used perfectly predicts the dependent variable.
The graph on the right, with an R² of 0.83, indicates that 83% of the variation in the dependent variable is explained by the independent variable. In other words, all the variance in the data cannot be accounted for by the linear model.
It is calculated using the formula: $\text{Percentage error} = \frac{|\text{Experimental value} - \text{Theoretical value}|}{\text{Theoretical value}} \times 100 %$
| Do | Don't |
|---|---|
| Propagate the uncertainties correctly and to the correct precision | Include any measurements in error propagation which do not affect the outcome |
| Deal appropriately with outliers in the data | Forget or leave out outliers in the data |