TOK physics: Data handling
Knowledge questions
How do visual representations of data enhance our interpretation of it?
To what extent do uncertainties limit our ability to interpret data?
How can we be certain that our interpretation of data is true?
In physics we test relationships by drawing graphs. A graph gives a visual representation that is much easier to interpret than the numbers themselves especially if there are uncertainties. Here are some examples based on bags of balls.
You are given 20 bags containing random numbers of balls, you weigh them all and plot the results in a table.
Here is the data in an excel file.
- What is the most probable mass of 1 ball?
You can do this by looking at the data but it's not easy.
Now put the list in order and plot a bar chart.
- Is it easier to see the mass of one ball now?
- What is the mass of the bag?
- Could the balls have a different mass?
- How could you be more certain that your answer is correct?
The smallest difference is 23g this is the most likely mass of a ball. The masses are not multiples of 23 though, this is because the bag has a mass of 3 g. Subtract 3 from the masses and they are all multiples of 23 g.
The mass of a ball could be 11.5 g but then then all the bags had even numbers of balls, this is unlikely since the number is random. To be more certain you should weigh more bags.
This is very much like the way Millikan found the charge of an electron. He measured the charge of many oil drops and looked for the largest common factor
You are now given 20 more bags with the number of balls printed on the bag. Here is a table of number and mass.
- One of these is incorrect, can you spot which one?
Now plot an x-y scatter using the data. Add a trend line by right clicking one of the points and selecting "add trend line"
- Can you see the incorrect one now?
- What mistake has been made?
- Is their any other possible explanation?
The data for 82 balls is wrong, it should be 83 balls. It could also be explained by a mistake in weighing the bag but this is unlikely.
The measurements were repeated using a kitchen balance that only measured to the nearest 50 g.
- Plot a graph for this data with a trend line. Can you see the mistake now?
The uncertainties (± 50 g) hide the mistake.
The experiment was repeated but this time using potatoes instead of balls.
- What can you deduce from this data?
The potatoes are not the same mass since there is not a linear relationship between number and mass.
You will have conclude that it is better to have more sensitive data but this is not always the case.
Which of the 12 concepts are related to this activity?
- evidence
- certainty
- truth
- interpretation
- power
- justification
- explanation
- objectivity
- perspective
- culture
- values
- responsibility