Processing data in Physics (DP IB Physics): Revision Note

Processing data in Physics

• This is the "calculation" phase of your investigation

• Data processing involves applying mathematical calculations to your raw data to determine the final values you need to answer your research question

  • For example, calculating a period, a resistance, or an acceleration due to gravity

Principles of data processing

Carry out relevant and accurate data processing

• The goal of data processing is to carry out relevant and accurate calculations to transform raw data into a form which is easier to interpret

  • This involves calculating mean values, propagating uncertainties, and presenting the results clearly

• Show your working clearly

  • For every type of calculation you perform, you must show one full, worked example

• Calculating an average

  • When you have repeat trials, you must calculate an average (mean) value to use in further calculations

  • You should exclude any anomalous results from your average

• Propagating uncertainties

  • The uncertainties from your raw measurements must be carried through your calculations to find the uncertainty in your final, processed result

  • For addition or subtraction, add the absolute uncertainties.

    • Example: To find the length of an object, you measure final position - initial position on a ruler

    • The uncertainty in is (uncertainty of final position) + (uncertainty of initial position)

    • For a ruler, this is 0.5 mm + 0.5 mm = 1 mm

  • For multiplication or division, add the fractional or percentage uncertainties.

    • Example: To determine the resistance of a component, you would measure potential difference and current and calculate using

    • The % uncertainty in is (% uncertainty in ) + (% uncertainty in )

  • For quantities that are raised to a power, multiply the fractional or percentage uncertainty by the power

    • Example: To determine the kinetic energy of an object, you would measure mass and speed and calculate using

    • The % uncertainty in is (% uncertainty in ) + 2×(% uncertainty in )

• Significant figures

  • Your final calculated answer should be given to a number of significant figures that reflects the precision of the raw data used

    • The general rule is that your final answer should have the same number of significant figures as the least precise piece of data used in the calculation

Presenting data in tables

• Your processed data should be presented in a neat, clearly labelled table

  • It is good practice to show the raw data and processed data in the same table

• Tables must include:

  • a descriptive numbered title

    • For example, "Table 1: Time taken for 20 swings of varying lengths of a pendulum"

  • appropriate column headers

    • For each variable, include the name of the quantity, the unit of measurement, and the absolute uncertainty (using the ± symbol)

    • The independent variable should be in the first column, followed by the dependent variables in subsequent columns

  • all the raw and processed data

    • For each variable, all recorded data should have the same number of decimal places

    • The number of significant figures used for the data should also be consistent with the quoted uncertainties

Presenting data graphically

• A graph is the most powerful tool for representing your results

  • It turns lists of numbers into a clear visual pattern

• A correctly formatted scientific graph must include:

  • a descriptive title

    • For example, "A graph to show the relationship between the period squared and the length of a simple pendulum"

  • labelled axes with units

    • The independent variable is plotted on the x-axis

    • The dependent variable is plotted on the y-axis

  • an appropriate scale

    • Both axes should begin at the origin (0, 0), but if not, you should justify why

    • The scale should be chosen so that plotted points take up at least half of the space

  • clearly plotted data points

    • These should be small crosses or points

    • If using points, drawing a circle around them can ensure they are not missed

  • error bars

    • These represent the absolute uncertainty in the measurements

    • If the uncertainty is too small to show as an error bar on a graph, then it may be omitted

  • a line (or curve) of best fit

    • This shows the overall trend in the data

    • This line does not have to go through every single point, but it must go through all the error bars

Linearisation

• Many relationships in physics are not linear, resulting in a curve when plotted.

• It is difficult to determine the exact relationship from a curve, so we linearise the data.

• This involves manipulating the data based on a known physical formula so that it produces a straight line when plotted.

  • For example, the formula for a pendulum is T = 2π√(L/g).

  • This can be rearranged to T² = (4π²/g)L

  • This is in the form of a straight-line equation, y = mx + c.

  • By plotting T² (y-axis) against L (x-axis), you should get a straight line through the origin with a gradient (m) equal to 4π₂/g.