top of page

# 1.2. Uncertainties and Errors

As mentioned in the previous section, Physicists are all about measuring stuff in the world. However, it is also important that we consider the errors associated with this measurement - so that we can be confident that our measurement is sufficiently accurate and precise (these are not the same thing). When we take a measurement, we have an associated uncertainty with that measurement, depending on how precise our equipment is. This section talks about sources of uncertainty in measurements and how we deal with these. As well as being important for doing good practical Physics work, this stuff is also super important for your IA and the experimental section of Paper 3.

â€‹

I've broken this section up as follows:

â€‹

Random & Systematic Error

#### Random and Systematic Errors

When I take a measurement, there are many sources of error that we must account for.  Examples of sources of error include not zeroing a set of weighing scales before measuring, a meniscus error when measuring a volume in a measuring cylinder or a measuring tape that has been stretched out over time.

We can characterise these errors as either Random or Systematic.

â€‹

• Random Errors are caused by unknown and unpredictable changes in the experiment, e.g. electromagnetic noise when measuring tiny currents in a circuit.

â€‹

• Systematic Errors are regular and caused by errors in the equipment or use of the equipment. These can be fixed (e.g. a zero error on a scale), or scaled (e.g. a metre rule swelling).

â€‹

â€‹

When discussing measurements for an experiment we can assess whether they are accurate or precise, which is something which has a lot of common misconceptions.

â€‹

• Accuracy is how close to the true value a measurement is. For example, if I properly calibate a mass balance, it can be said to produce accurate measurements. Reducing systematic errors improve the accuracy of a measurement.

â€‹

• Precision is how close together multiple measurements are. For example, if multiple current readings in a circuit all give values within 0.02 A the measurements can be said to be precise. Reducing the random errors improve the precision of a measurement.
(N.B. Precision is also used to discuss the number of significant figures a measurement is given to, e.g. using the cm or mm scale)â€‹

## Video Lessons

 Chris Doner Accuracy and Precision Gradepod Precision IB Specific Physics Online Accuracy, Precision Study Nova Accuracy, Precision and Error Study Nova Accuracy and Precision

## Resources

 IB Physics Topic 1 Notes IB-Physics.net Chapter 1 Summary IB Revision Notes Mr. G 1.2 Teaching Notes 1.2 Student Notes Physics and Maths Tutor Measurements Definitions Measurements Key Points Measurements Detailed Notes Measurements Flashcards A Level Resources - content slightly different

## Questions

 Grade Gorilla 1.2 (Errors) MCQs Topic 1 (Measurements) Final Quiz Quick IB Specific Mixed MCQs Isaac Physics Accuracy, Percentage Difference and Reliability Mr. G 1.2 Formative Assessment Topic 1 Summary Qs IB Specific Questions
Presenting Uncertainties

#### Presenting Uncertainties

We now need to quantify these uncertainties for useful measurements. Imagine I want to find the length of a Mars Bar. I choose to use the 'cm' side of a 30 cm ruler and find the length to be 11 cm. The absolute uncertainty of my measurement is ± 1 cm, as this was the uncertainty in my measurement scale. We always quote our measurements with their associated uncertainty

i.e. 11 cm ± 1 cm.

â€‹

The standard notation we use is:

â€‹

x ± Δx

â€‹

Where:

x = measurement     (e.g. 11 cm)

Δx = absolute uncertainty (e.g. ± 1 cm)

â€‹

For this Mars Bar example, I measured the length to the nearest cm. However, if I decide to accurately quote the height of Mount Everest to the nearest cm that would be a far more impressive feat - because the fractionaI uncertainty (i.e. uncertainty as a fraction of the actual measurement) would be much, much smaller.

## Video Lessons

 Physics Online Absolute Uncertainty % Uncertainty - Single Reading % Uncertainty - Multiple Reading Science Shorts Uncertainties Study Nova Absolute, fractional, percentage uncertainty

## Resources

 IB Physics Topic 1 Notes IB-Physics.net Chapter 1 Summary IB Revision Notes Mr. G 1.2 Teaching Notes 1.2 Student Notes Physics and Maths Tutor Measurements Definitions Measurements Key Points Measurements Detailed Notes Measurements Flashcards A Level Resources - content slightly different

## Questions

 Dr French's Eclecticon Data Analysis Problems Data Analysis Solutions Excel Solutions Link to Dr French's Site Extension: Pre-University Material Grade Gorilla 1.2 (Errors) MCQs Topic 1 (Measurements) Final Quiz Quick IB Specific Mixed MCQs Isaac Physics Absolute Uncertainties Relative Uncertainties Mr. G 1.2 Formative Assessment Topic 1 Summary Qs IB Specific Questions
Propagating Uncertainties

#### Propagating Uncertainties

To go back to the Mars Bar example - if I now decide I'd like to calculate the volume of my Mars Bar, I might decide to use the equation for volume of a cuboid: length x width x height. However, each measurement of a dimension has an uncertainty associated with it. This section teaches us how we can deal with these propagating uncertainties if we have multiple measurements to consider.

â€‹

There are a standard set of rules to follow when propagating the size of uncertainties, so this section walks us through them.

## Video Lessons

 Physics Online Combining Uncertainties Worked Example Science Shorts Combining Uncertainties Study Nova Calculating Uncertainties

## Resources

 IB Physics Topic 1 Notes IB-Physics.net Chapter 1 Summary IB Revision Notes Mr. G 1.2 Teaching Notes 1.2 Student Notes Physics and Maths Tutor Measurements Definitions Measurements Key Points Measurements Detailed Notes Measurements Flashcards A Level Resources - content slightly different

## Questions

 Dr French's Eclecticon Data Analysis Problems Data Analysis Solutions Excel Solutions Link to Dr French's Site Extension: Pre-University Material Grade Gorilla 1.2 (Errors) MCQs Topic 1 (Measurements) Final Quiz Quick IB Specific Mixed MCQs Isaac Physics Propagating Uncertainties Mr. G 1.2 Formative Assessment Topic 1 Summary Qs IB Specific Questions
Graphical Skills

#### Graphical Skills

While we are talking about all this stuff to do with taking experimental measurements, it makes sense to actually think how we can present this data properly - i.e. in a graph.

This is a really skill in Physics (again big part of the IA marking scheme, as well as the experimental bit of Paper 3).

â€‹

What a graph really is useful for is identifying a mathematical relationship between two variables. When we plot a line of best fit, we are essentially 'averaging' multiple points to see the trend more clearly.  At GCSE we were confident about plotting the Independent variable on the x-axis and the Dependent variable on the y-axis. Now, at the IB we need to use the equation of a straight line,

y = mx + c to identify what different parts of my linear line of best fit actually represent.

If my trendline is not a straight line (consider the shapes of  y = √x  or y = x²) I can linearise it - that is manipulate what I plot on my x- or y- axes to ensure I plot a straight line.

## Video Lessons

 Gradepod Linearising Graphs IB Specific Physics Online Drawing Graphs Calculating Gradients & Intercepts Study Nova Linearisation Linearisation (Lecture)

## Resources

 IB Physics Topic 1 Notes IB-Physics.net Chapter 1 Summary IB Revision Notes Mr. G 1.2 Teaching Notes 1.2 Student Notes Physics and Maths Tutor Measurements Definitions Measurements Key Points Measurements Detailed Notes Measurements Flashcards A Level Resources - content slightly different

## Questions

 Grade Gorilla 1.2 (Errors) MCQs Topic 1 (Measurements) Final Quiz Quick IB Specific Mixed MCQs Isaac Physics Gradients and Intercepts Equations of Graphs Area under a Curve I Area under a Curve II Mr. G 1.2 Formative Assessment Topic 1 Summary Qs IB Specific Questions
Uncertainties in Graphs

#### Uncertainties in Graphs

As with any measurement, the gradient or intercept of a graph we draw will have an associated uncertainty. For example, later we will look at using a length/ resistance graph to calculate the resistivity of a certain material by finding the gradient, so it is important we are able to calculate the uncertainty associated with this value.

â€‹

As an aside, if you are unfamiliar with Microsoft Excel, I would certainly advise spending a bit of time getting to grips with how to plot graphs and obtain the equations the trendlines.

â€‹

## Video Lessons

 Physics Online Uncertainties in Gradients Science Shorts Uncertainties (Graphs)

## Resources

 IB Physics Topic 1 Notes IB-Physics.net Chapter 1 Summary IB Revision Notes Mr. G 1.2 Teaching Notes 1.2 Student Notes Physics and Maths Tutor Measurements Definitions Measurements Key Points Measurements Detailed Notes Measurements Flashcards A Level Resources - content slightly different

## Questions

 Grade Gorilla 1.2 (Errors) MCQs Topic 1 (Measurements) Final Quiz Quick IB Specific Mixed MCQs Mr. G 1.2 Formative Assessment Topic 1 Summary Qs IB Specific Questions