What you need to know
- Unit 3Use correct units and an appropriate number of significant figures when results are processed.
Graph plotting is the next lesson. This lesson stops at the table. Illustrative numbers are not experimental results.
By the end, you should be able to…
- Place the independent variable in the first column and units in the headings.
- Keep raw readings separate from means and rates.
- Process a short table without adding precision.
Build your understanding
Headings do the labelling once
Each column needs a heading with the quantity and the unit. The unit sits in the heading, not beside every number. An illustrative heading is “Temperature / °C” or “Time / s”. The independent variable usually occupies the first column, in the order it was changed.
A heading such as “Amount” is too vague. Say mass, volume, time or rate, and the unit. A rate heading has a compound unit, such as cm³ min⁻¹ or s⁻¹. Leaving the unit only in the first row of data makes the column harder to check and is a common reason a table is unclear.
Raw, then processed
Repeats deserve their own columns, or clearly separated entries, so a reader can see the scatter. The mean is a further column. Do not overwrite a raw value with the mean. An anomalous reading can stay visible and be left out of the mean only if you say so.
Illustrative times of 40, 42 and 44 s have the mean (40 + 42 + 44) ÷ 3 = 42 s. A later rate column might be 1 ÷ mean time if the question defines rate that way. State the definition. Do not invent a rate unit the question did not use.
Do not upgrade the precision
If the readings are whole seconds, a mean of 41.6666… s should be reported as 42 s, or as 41.7 s if one extra decimal place is justified while you show the unrounded working. A percentage calculated from those times should not gain a string of digits.
Use the same decimal places down a column of the same instrument. Mixing 5, 5.0 and 5.00 implies three different resolutions. Processed columns can differ from raw columns, but each column should be consistent with the rule you stated.
| Temperature / °C | Time 1 / s | Time 2 / s | Mean time / s |
|---|---|---|---|
| 20 | 48 | 52 | 50 |
| 30 | 31 | 33 | 32 |
| 40 | 22 | 46 | leave 46 out if checked as inconsistent; otherwise do not hide it |
Graph skills: SLAPUK and choosing a scaleFrom table to graph: table headings become your axis labels.
Make your reasoning visible
Unit in the heading
Write the unit once. If you need two units, you need two columns or a compound unit, not a mixture inside the cells.
Show the step you were asked for
If the question says calculate the mean, the mean column is the answer. If it says calculate the rate, add a rate column and state the formula.
Avoid this misconception
The claim: The mean replaces the repeats, so the raw numbers can be rubbed out.
The correction: The raw numbers are the evidence for the mean and for any anomaly. Keep them, and show the processed column beside them.
Check your understanding
Try each question before opening the suggested answer.
Practice question
Retrieval and explanation · suggested answer
Illustrative repeat masses of product are 0.12 g, 0.14 g and 0.13 g. Calculate the mean and say how it should be written.
Show suggested answer
(0.12 + 0.14 + 0.13) ÷ 3 = 0.39 ÷ 3 = 0.13 g. Write 0.13 g, matching the two decimal places of the readings. Do not write 0.13000 g.
Practice question
Retrieval and explanation · suggested answer
A student heads a column “Rate” and writes 0.04, 0.05 and 0.03. What is missing?
Show suggested answer
The unit. The heading should state the rate unit, for example cm³ s⁻¹ or s⁻¹, so the numbers can be interpreted.
Practice question
Retrieval and explanation · suggested answer
Why is the independent variable placed in the first column?
Show suggested answer
The table is then read in the order the factor was changed, which is also the usual order for plotting that factor on the x-axis. It keeps the outcome columns as the measurements.
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 gives the volume of DCPIP decolourised as 2.0 cm³ and the juice titres as 8.0, 8.4 and 12.8 cm³. Calculate the mean titre you would use, and the relative vitamin C comparison if concentration is taken as proportional to 1/titre. State what you did with 12.8 cm³.
Show a hint
Decide whether 12.8 cm³ is consistent before you average.
Explore the reasoning
8.0 and 8.4 cm³ agree. 12.8 cm³ is inconsistent and should be checked or repeated. If it is excluded after that decision, the mean of the remaining titres is (8.0 + 8.4) ÷ 2 = 8.2 cm³. A smaller titre means a higher vitamin C concentration when the DCPIP volume is the same, so this juice would be compared using 1/8.2 rather than using a mean dragged up by 12.8. The assumption is that 12.8 cm³ was checked and not reproduced.
Recall this lesson
Lesson recall questions
Question 1 of 5: A graph of absorbance against time is a straight line through the origin for the first 60 s of a beetroot investigation. Outline, in order, how to find the initial rate using a large triangle.
Unit 3 processing results
Practice question
Retrieval and explanation · suggested answer
A graph of absorbance against time is a straight line through the origin for the first 60 s of a beetroot investigation. Outline, in order, how to find the initial rate using a large triangle.
Lesson: R2: Scales, lines and gradients
Build the sequence from memory first. Then reveal the model order.
Tap the steps in the order you recall. Tap a placed step to send it back.
- 01Next step
- 02Waiting
- 03Waiting
Tap to place
Beyond the classroomThe unit is part of the quantityMeasurement · units · Enrichment, not required recall
The organisations that maintain the SI treat the unit as part of how a quantity is stated. In a school table the same rule is practical: a heading without a unit is an unfinished measurement, even when the arithmetic is right.
Back to the spec: Unit 3 processing: use correct units throughout. Put them in the column headings and in any rate you calculate.
BIPM: measurement unitsQuestion
A mean is calculated correctly as 0.13 but the column has no unit. Is the processing finished?
Explore a possible response
No. 0.13 g and 0.13 kg are not the same result. The unit has to travel with the processed number, usually in the heading of that column.