Presenting Observations & Data
- Data can be presented in a variety of ways, such as on graphs, charts, or tables
- Tables are applicable to any experiment yielding data
- Graphs, on the other hand, are a little trickier depending on the type of data collected e.g. quantitative or qualitative
- Quantitative data uses numerical values
- Qualitative data is observed but not measured with a numerical value e.g. colour
Presenting Data in a Table
- When taking readings, a sensible range should be taken, and the values should all be stated to an appropriate number of significant figures or decimal places
- This is usually the same number as the resolution of the measuring instrument
- The columns in any table should have both a quantity and a unit in their heading
- When labelling columns, the names of the quantities should be separated from their unit by a forward slash ( / )
- For data displayed in a table:
- The first column should contain the independent variable
- The second column should contain the dependent variable
- If repeat readings of the dependent variable are required, these should be included with a column for the mean value at the end
- Any columns required for processing data e.g. calculations should come after this
Conventions for presenting data in a table. The length is the independent variable and the frequency is the dependent variable
Presenting Data on a Graph
- All readings, including suspected anomalous results, should be plotted on a graph so that they can be easily identified
- When taking repeat readings, it is the mean value that is plotted
- The way data is presented on a graph depends on what type of data it is
- Only certain values can be taken, normally a whole number e.g. number of students
- This should be displayed on a scatter graph or bar chart
- Can take any value on a scale e.g. voltage in a circuit
- This should be displayed on a line or scatter graph
- Values that can be sorted into categories e.g. types of material
- This should be displayed on a pie or bar chart
- Data that can be put in ordered categories e.g. low, medium, high
- This should be displayed on a bar chart
Processing, Analysing & Interpreting Experimental Results
- After an experiment has been carried out, sometimes the raw results will need to be processed before they are in a useful or meaningful format
- Sometimes, various calculations will need to be carried out in order to get the data in the form of a straight line
- This is normally done by comparing the equation to that of a straight line: y = mx + c
Worked Example
A student measures the background radiation count in a laboratory and obtains the following readings:
The student is trying to verify the inverse square law of gamma radiation on a sample of Radium-226. He collects the following data:
Use this data to determine if the student’s data follows an inverse square law.
Step 1: Determine a mean value of background radiation
- The background radiation must be subtracted from each count rate reading to determine the corrected count rate, C
Step 2: Compare the inverse square law to the equation of a straight line
- According to the inverse square law, the intensity, I, of the γ radiation from a point source depends on the distance, x, from the source
- Intensity is proportional to the corrected count rate, C, so
- The graph provided is of the form 1/C–1/2 against x
- Comparing this to the equation of a straight line, y = mx
- y = 1/C–1/2 (counts min–1/2)
- x = x (m)
- Gradient = constant, k
- If it is a straight line graph through the origin, this shows they are directly proportional, and the inverse square relationship is confirmed
Step 3: Calculate C (corrected average count rate) and C–1/2
Step 4: Plot a graph of C–1/2 against x and draw a line of best fit
- The graph shows C–1/2 is directly proportional to x, therefore, the data follows an inverse square law
