What you need to know
- Unit 3Comment on the number of readings, the range of measurements, and whether the significant figures match the measurements.
You are usually commenting on someone else’s method, not writing your own from a blank page. Processing the numbers comes in the next skills group. Do not treat a comment as a significance test.
By the end, you should be able to…
- Judge whether there are enough readings to see a pattern.
- Judge whether the range and intervals can support the claim.
- Comment on significant figures using the least precise measurement.
Build your understanding
How many readings, and why
A comment needs a reason. Two temperatures can show that those two results differ. They cannot show the shape of a relationship, a peak, or a plateau. Five or more values, spread across the range you care about, can show a rise and a levelling off. Say which of those claims the method can support.
Repeats at the same value are not the same thing as more values of the independent variable. Three repeats at one pHA measure of how acidic or alkaline a solution is, based on its H⁺ ion concentration. Below 7 is acidic, above 7 is alkaline. tell you about scatter at that pH. They do not map pH. A strong comment names which of the two is missing.
Range and interval are different
The range is the span from the lowest to the highest value. The interval is the gap between neighbouring values. An illustrative series of 20, 21, 22, 23 and 24 °C has a narrow range even though there are five readings. It cannot support a conclusion about enzymeA globular protein that acts as a biological catalyst, speeding up a specific reaction. from 0 °C to 60 °C.
A series of 0, 20, 40, 60 and 80 °C has a wider range but may miss a sharp optimum between 20 and 40 °C. If the question’s claim is about an optimum, say that intermediate values are needed. Do not praise a range merely because the numbers look neat.
Figures follow the instrument
Comment when the recorded figures pretend to more precision than the measurements. A time read to the nearest second should not be processed into a rate quoted to five decimal places. A length read as 12 mm should not become 12.000 mm.
When values are multiplied or divided, the result is limited by the least precise measurement, judged by significant figures. When values are added, decimal places usually set the limit. State the rule you are using. The specification does not make one fixed number of significant figures correct for every table.
Make your reasoning visible
Quote what you were shown
“Only two concentrations were used, so a straight-line relationship cannot be established” uses the evidence. “They should have done it better” does not.
Separate range from repeats
Ask: more values along the axis, or more trials at each value? The improvements are different.
Avoid this misconception
The claim: More readings always means a better range.
The correction: Readings clustered together can be numerous and still cover only a narrow range. Range is the span. Repeats are extra trials at a value.
Check your understanding
Try each question before opening the suggested answer.
Practice question
Retrieval and explanation · suggested answer
An illustrative student records the rate of an enzyme at 30 °C and 32 °C only, then writes that the rate increases with temperature up to an optimum and then falls. What is wrong with the claim?
Show suggested answer
The range is only 30 to 32 °C, and there are only two values. That cannot show an optimum or a fall after it. It can support a comparison of those two temperatures only.
Practice question
Retrieval and explanation · suggested answer
Times in seconds are 42, 45 and 47. A student reports the mean as 44.6667 s. Comment on the significant figures.
Show suggested answer
The times are whole seconds, so the mean should not be given to four decimal places. 44.7 s to one decimal place, or 45 s to the nearest second, matches the measurements more honestly. 44.6667 claims a precision the stop-clock readings do not have.
Practice question
Retrieval and explanation · suggested answer
Five repeats are taken at pH 7 and none at any other pH. Can the student conclude how pH affects the rate?
Show suggested answer
No. The repeats describe scatter at pH 7. There is no range of pH, so there is no evidence of an effect of pH.
Take the idea further
Apply the same specification knowledge to an unfamiliar problem. Any extra assumptions are supplied in the question.
Stretch question
An unfamiliar table uses light distances of 10, 20, 30, 40 and 50 cm, one reading at each distance, and concludes that the rate is inversely proportional to distance. What can you support, and what extra readings would you ask for? Assume bubble counts are the dependent variable.
Show a hint
Two issues are mixed: the shape of the relationship, and the lack of repeats.
Explore the reasoning
Five distances can suggest a pattern, but one reading at each distance cannot show whether a point is reliable, and five points do not by themselves prove inverse proportion. Repeats at each distance would show scatter. A check of inverse proportion needs a stated graph, such as rate against 1/distance, not only the raw distances. The assumption is that no other variable was changed.
Recall this lesson
Lesson recall questions
Question 1 of 5: A thermometer used in an enzyme water bath has scale divisions of 1 °C. State the resolution of the instrument.
Unit 3 implementation and measurements
Practice question
Retrieval and explanation · suggested answer
A thermometer used in an enzyme water bath has scale divisions of 1 °C. State the resolution of the instrument.
Lesson: I1: Readings, range and significant figures
Try this from memory first.
Beyond the classroomThe definition of a unit is not the resolution of your rulerMeasurement · standards · Enrichment, not required recall
Standards laboratories define the metre with great care. A school ruler is still read to its own smallest division. Reporting extra digits does not borrow the precision of the international definition.
Back to the spec: Unit 3 implementation: comment on significant figures in the readings you are shown. The figures come from the instrument in the method, not from the definition of the unit.
National Physical Laboratory: the metreQuestion
A length is measured with a ruler marked in millimetres and reported as 14.3852 mm. Why is that report misleading?
Explore a possible response
The ruler was not read to ten-thousandths of a millimetre. Extra digits imply a resolution the instrument did not have. The record should stop at the precision of the reading, such as the nearest millimetre.