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I.2.2 Processing data in Physics — IB Physics HL Revision Notes & Topical Questions

5 min read 10 parts Lesson 19 of 22 1 quiz

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Lesson summary

I.2.2 Processing data in Physics — IB PHYSICS SL notes: Process raw data using means, propagated uncertainties, correct significant figures, tables, graphs and linearisation.This is the "calculation" phase — applying mathematics to raw data to get the values needed.Calculations t…

  • Show clear working
  • Addition or subtraction
  • Multiplication or division
  • Quote the uncertainty to one significant figure
  • A descriptive numbered title
  • Independent variable in the first column

Part 1 of 8Aim of data processing

1This is the "calculation" phase
  • This is the "calculation" phase applying mathematics to raw data to get the values needed.
2
Calculations transform raw data into a form that is easier to interpret.
  • Examples are a period, a resistance or the acceleration due to gravity.
3Show clear working
  • Show clear working one full worked calculation for each type of calculation, even if a spreadsheet is used.

Part 2 of 8Mean values

Mean values
With repeat trials, calculate the mean for use in further calculations.
Exclude anomalous results from the mean.
Where the period comes from many oscillations, divide the mean time by the number of oscillations.
  • The count of oscillations is exact, so the percentage uncertainty is unchanged.

Part 3 of 8Propagating uncertainties

Propagating uncertainties
Carry raw-data uncertainties through the calculation to the final result.
Addition or subtraction
  • Addition or subtraction add the absolute uncertainties.
  • A length from two ruler readings has 0.5 mm + 0.5 mm = 1 mm.
Multiplication or division
  • Multiplication or division add the fractional or percentage uncertainties.
  • R = V/I has %R = %V + %I.
Power
  • Power multiply the percentage uncertainty by the power.
  • Ek = ½mv2 has %Ek = %m + 2 × %v.
Quote the uncertainty to one significant figure
  • Quote the uncertainty to one significant figure and the result to the same decimal place as the uncertainty.

Part 4 of 8Significant figures

Significant figures
Processed results must reflect the precision of the raw data.
The final answer has the same number of significant figures as the least precise data used.
Never copy the full calculator display.

Part 5 of 8Presenting data in tables

1
Show raw and processed data together in a neat, labelled table.
2A descriptive numbered title
  • A descriptive numbered title e.g. Table 1: time for 20 swings for different pendulum lengths.
3
Column headers with the quantity, its unit and the absolute uncertainty (±).
4Independent variable in the first column
  • Independent variable in the first column dependent variables after it.
5
Consistent decimal places in each column.
  • Significant figures consistent with the quoted uncertainties.

Part 6 of 8Presenting data graphically

Presenting data graphically
A graph turns numbers into a clear visual pattern.
A descriptive title
  • A descriptive title e.g. a graph to show the relationship between T2 and L.
Labelled axes with units
  • Labelled axes with units independent variable on x, dependent variable on y.
An appropriate scale.
  • Begin at (0, 0), or justify why not.
  • Points should take up at least half the space.
Clearly plotted data points
  • Clearly plotted data points small crosses or circled points.
Error bars for the absolute uncertainty
  • Error bars for the absolute uncertainty omitted only if too small to show.
A line or curve of best fit
  • A line or curve of best fit through all the error bars but not joining the dots.

Part 7 of 8Linearisation

1Many relationships are curves
  • Many relationships are curves it is hard to find the exact relationship from a curve.
2Rearrange using a known formula so the graph is a straight line y
Rearrange using a known formula so the graph is a straight line y mx + c.
3Pendulum: T
2π√(L/g) becomes T2 = (4π2/g)L.
  • A graph of T2 (y) against L (x) is a straight line through the origin with gradient 4π2/g.
4
The independent variable always goes on the x-axis.

Part 8 of 8More from the specification

1
Recording Raw Experimental Data
  • In scientific investigations, raw measurements must be recorded directly in a structured table alongside their associated instrumental uncertainties.
    • (such as potential difference V and current I)
2
Calculating Mean Values and Minimizing Random Errors
  • Conducting multiple repeat trials for each measurement allows calculation of an average value, mitigating random errors and improving experimental accuracy.
3
Qualitative Observations vs Quantitative Data
  • Complete scientific reports combine quantitative numerical measurements with detailed qualitative observations, noting relevant visual changes such as gas evolution or color transitions.
4
Trend Identification and Graph Processing
  • Processed experimental data is plotted on coordinate axes to visualize the underlying trend, enabling mathematical modeling and testing of theoretical physical relationships.
5
Qualitative
  • Descriptive and not numerical.
6
Current
  • Flow of electrons in a circuit.
7
Potential difference
  • Work done by a unit charge passing through a component.
8
Simple pendulum
  • A small bob on a light string of length L
9
Random error
  • An unpredictable variation in readings, reduced by repeating and averaging.
10
Directly proportional
  • Two quantities increase together in a constant ratio, giving a straight line through the origin.

Key terms

TermMeaning
MeanSum of values divided by the number of values.
Propagation of uncertaintyCarrying uncertainties through a calculation.
Percentage uncertaintyAbsolute uncertainty divided by the value × 100%.
Error barLine on a graph showing the uncertainty of a point.
Line of best fitSmooth line or curve that represents the trend.
LinearisationRearranging a relationship to give a straight line.

Avoid these mistakes

1
Quoting results with more significant figures than the raw data.
2
Adding absolute uncertainties when multiplying — add percentage uncertainties.
3
Joining data points dot-to-dot instead of drawing a best-fit line.
4
Showing no worked calculation of how raw data became processed data.
5
Putting the dependent variable on the x-axis.

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