What you need to know
- Unit 6Plot data on a suitable scale with units, including a graph that may be logarithmic, describe the pattern, and find a gradient with a large triangle.
A straight line on a log axis is not a linear increase in the original counts. These figures are illustrative. A line of best fit is only for a section that is actually linear on the axes you are using.
By the end, you should be able to…
- Assign axes, units and an even scale that uses the grid.
- Explain what a logarithmic axis does, and when not to use one.
- Calculate a gradient from a large triangle and keep the unit.
Build your understanding
Axes and an even scale
Put the independent variable on the x-axis and the dependent variable on the y-axis. Label both with units. Choose a scale that uses a good share of the grid and has equal intervals. A scale that jumps from 10 to 50 to 60 compresses the pattern. The origin can be omitted if starting at zero would squash the points, but the scale must still be even and labelled.
Plot the points you were given, including one you have queried, unless the question tells you to omit an identified anomaly. If the points rise and then level off, do not force one straight line through all of them.
A log axis is for multiplication, not decoration
Unit 6 allows a graph that is logarithmic. Use it when the values span orders of magnitude or when you are looking for a constant ratio, such as a populationAll the individuals of one species living in one area at the same time. that doubles. Label the axis. “Number of bacteria” on a log₁₀ scale is not the same axis as the count itself.
Illustrative counts of 1×10³, 2×10³, 4×10³ and 8×10³ at hourly intervals double each hour. On a linear axis the line curves upwards. On a log₁₀ axis the steps are equal, because each doubling adds log₁₀(2), about 0.30, to the log value: about 3.00, 3.30, 3.60 and 3.90. A student who says the population “increases by 0.30 bacteria an hour” has read the logarithm as a count. An increase of 0.30 in log₁₀(N) means the count is multiplied by about 2.
A large triangle, in the units of the axes
On a straight section of a linear graph, draw a triangle that covers a large fraction of the line. Gradient = change in y ÷ change in x, read from the scales. Illustrative points (4 min, 8 cm³) and (12 min, 28 cm³) give a change in volume of 20 cm³ and a change in time of 8 min. Rate = 20 ÷ 8 = 2.5 cm³ min⁻¹. Dividing 28 by 12 would assume the line passes through the origin.
On a log axis the same arithmetic gives a change in the log value, not a change in the raw count, unless you convert back and the question asks for that. A curve on a linear grid needs a tangent at the stated time. The gradient of that tangent is the rate at that instant, not the mean rate for the whole curve.
NOT: a log step is not a count, and one straight line should not be forced through a plateau.
- Independent variable on the x-axis
- Label a log axis with its base
- A doubling adds about 0.30 to log10
- A large triangle is for a linear section
Two traps this diagram blocks
- Do not read 0.30 on a log10 axis as 0.30 extra bacteria.
- Do not draw one straight line through a rise and a later plateau.
From the diagram alone
Question
Bacterial counts double every hour and are plotted as log10 of the count. Explain why the line is straight, and what a step of about 0.30 means. [3]
Show a model answer
Each doubling adds log10 of 2, about 0.30, so the log values are equally spaced. A step of 0.30 means the count has been multiplied by about 2. It does not mean 0.30 bacteria were added.
Graph skills: SLAPUK and choosing a scaleMixed graph challenge: scales, keys, best fit and curves.
Make your reasoning visible
Read the axis title before the slope
A steep line on a cramped scale can be a small change. A straight line on a log scale can be a doubling, not a steady addition.
Large triangle, labelled changes
Mark the two coordinates. A triangle a few millimetres wide makes the reading of the gradient the largest uncertainty.
Key explanations
- Use an even scale that fills a good share of the grid.
- On a linear straight section, a rate is the change in y divided by the change in x from a large triangle, not a single point divided by another.
Avoid this misconception
The claim: A line of best fit should pass through every point, the origin, and any log values as if they were ordinary counts.
The correction: A best-fit line follows a linear pattern on the axes you have, with points scattered on both sides. It passes through the origin only if the evidence supports that. Log values need a log label and a log interpretation.
Check your understanding
Try each question before opening the suggested answer.
Practice question
Retrieval and explanation · suggested answer
An illustrative straight line passes through (4 min, 8 cm³) and (12 min, 28 cm³). Calculate the rate.
Show suggested answer
Change in volume = 20 cm³. Change in time = 8 min. Rate = 20 ÷ 8 = 2.5 cm³ min⁻¹. Do not divide 28 by 12.
Practice question
Retrieval and explanation · suggested answer
Bacterial counts double every hour and the student plots log₁₀ of the count. Why is a straight line expected, and what does a step of about 0.30 on that axis mean?
Show suggested answer
Each doubling adds log₁₀(2), which is about 0.30, so the log values are equally spaced and the line is straight. A step of 0.30 means the count has been multiplied by about 2. It does not mean 0.30 extra bacteria.
Practice question
Retrieval and explanation · suggested answer
The points rise from 10 to 40 arbitrary light units and then stay almost level to 100 units. Why is one straight line of best fit inappropriate?
Show suggested answer
The relationship is not linear across the whole range. A single straight line would hide the plateau. Describe the rise and the levelling off, or fit a line only to a section that is straight.
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 semi-log graph has time on a linear x-axis and log₁₀(population) on the y-axis. The line is straight and falls. What can you conclude about the population, and what must you not conclude about the gradient? No coordinates are supplied.
Show a hint
A straight line on this graph means a constant ratio, downwards.
Explore the reasoning
The population is decreasing by a constant ratio in each unit of time, so the decline is exponential rather than a fixed number of individuals per hour. The gradient is a change in log₁₀(population) per unit time. It is not the number of individuals lost per hour unless you convert back from the logarithm. The assumption is that the y-axis really is logarithmic and is labelled with the base.
Recall this lesson
Lesson recall questions
Question 1 of 5: State where units should appear when tabulating mean rate of photosynthesis in cm³ min⁻¹ against light intensity in lux.
Unit 6 analysis
Practice question
Retrieval and explanation · suggested answer
State where units should appear when tabulating mean rate of photosynthesis in cm³ min⁻¹ against light intensity in lux.
Lesson: A1: Tables, units and processed numbers
Try this from memory first.
Put your biology to work
Explore where these ideas appear in the world. Enrichment, not extra required recall.
A log scale is a last resort for clarity, and it must be obvious
A2 · Scales, log axes and gradientsOffice for National Statistics guidance says linear scales are easier to read than log scales, and that log scales should be avoided unless the data cannot be shown…Specification Unit 6 · AnalysisRead & use the scienceClose article
Why this matters
Office for National Statistics guidance says linear scales are easier to read than log scales, and that log scales should be avoided unless the data cannot be shown clearly another way. Official charts are not examination answers. The warning still helps: a log axis changes what a slope means, so it has to be labelled and chosen for a reason. A logarithmic axis can compress a range that spans several orders of magnitude. That can reveal a multiplicative pattern, but it can also make a rapid increase look less dramatic to a casual reader. State the axis scale and units before describing a gradient. For a straight line on a log-y graph, equal vertical steps mean equal ratios rather than equal additions; it is not an ordinary linear increase.
Back to the specification
Pearson Edexcel IAL Biology · Issue 2, February 2021 · Unit 6, pp. 39–42. The application extends beyond required recall.
- Unit 6 · Analysis Tabulate, calculate, graph and interpret data, including possible logarithmic scales, gradients, uncertainty and realistic modifications.
Use the science
Why can a log scale make a multiplying population look like a steady straight line?
Explore a possible response
Equal steps on a log axis are equal multiplications. A population that doubles at a constant interval becomes evenly spaced on a log scale, so the line looks straight even though the raw counts are accelerating.
Explore the source
- Office for National Statistics: chart axes and gridlinesOffice for National Statistics
A growth curve can hide its scale
A2 · Scales, log axes and gradientsResearchers studying bacterial growth often plot optical density against time and use logarithmic transformations when populations span a wide range. A study of high-throughput growth measurements discusses lag…Specification Unit 6 · AnalysisRead & use the scienceClose article
Why this matters
Researchers studying bacterial growth often plot optical density against time and use logarithmic transformations when populations span a wide range. A study of high-throughput growth measurements discusses lag time and maximum growth rate in culture. Core Practical 13 gives this biological context, while Unit 6 analysis asks you to choose an appropriate graph scale and interpret its gradient. A straight segment on a log-transformed y-axis indicates approximately constant proportional growth, not a fixed number of new cells each minute. Axis labels must disclose the transformation.
Back to the specification
Pearson Edexcel IAL Biology · Issue 2, February 2021 · Unit 6, pp. 39–42. The application extends beyond required recall.
- Unit 6 · Analysis Tabulate, calculate, graph and interpret data, including possible logarithmic scales, gradients, uncertainty and realistic modifications.
Use the science
If an OD series doubles at equal time intervals, why might log(OD) against time look straight while raw OD against time curves upward?
Explore a possible response
Equal multiplications become equal additions after taking logs. Raw OD gains larger absolute amounts each interval, so the untransformed graph bends upward.
Explore the source
- Environmental factors in high-throughput bacterial growth measurementsPeer-reviewed study (PMC)