5.3.4Tools
Graphing in Biology — IB Biology SL Revision Notes & Topical Questions
5 min read 6 parts Lesson 10 of 10
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Part 1 of 6Choosing and Plotting a Graph
The type of graph must match the type of data, and every graph follows the same plotting conventions.
Line graph
- Line graph Use when both variables are continuous, such as volume of gas against time, and draw a smooth line or curve of best fit.
Bar chart
- Bar chart Use when the independent variable is a category, such as different species or tissue types, so the bars are separated.
Histogram
- Histogram Use for the frequency of a continuous measurement divided into classes, so the bars touch each other.
Scatter graph
- Scatter graph Use to look for a correlation between two measured variables, with a line of best fit added only if a trend exists.
Axes
- Axes Put the independent variable on the x-axis and the dependent variable on the y-axis, each labelled with quantity and unit.
Scales
- Scales Use even linear scales that let the points fill most of the grid, and plot points accurately in pencil.
| Data | Graph type | Bars or line |
|---|---|---|
| Categories (species) | Bar chart | Separate bars |
| Frequency of classes | Histogram | Touching bars |
| Two continuous variables | Line or scatter | Line or curve of best fit |
| Parts of a whole | Pie chart | Sectors |
Part 2 of 6Lines of Best Fit
A line of best fit shows the trend; it is not a join-the-dots line.
Lines of Best Fit
Shape
- Shape It may be straight or a smooth curve, depending on the trend that the plotted points actually follow.
Balance
- Balance Roughly equal numbers of points should lie above and below the line, and it need not pass through every point.
Origin
- Origin Force the line through (0,0) only when the biology says a zero value of x must give a zero value of y.
Anomalies
- Anomalies Circle clearly anomalous points and ignore them when drawing the line, then explain them in the analysis.
Part 3 of 6Reading Information from a Graph
Features of a graph carry biological meaning once you know how to read them.
1
The gradient of a straight line equals the change in y divided by the change in x, and it represents a rate.
2
On a curve the gradient keeps changing, so draw a tangent at the chosen point with a ruler and find its gradient.
3
The initial rate of an enzyme reaction is the gradient of the tangent drawn at time zero, where the substrate is not yet used up.
4
Intercepts are where the line crosses an axis, and maxima and minima are peaks and troughs where the gradient changes sign.
5
Interpolation estimates values between plotted points, whereas extrapolation extends the line beyond the data and is less reliable.
6
Uncertainty bars show the absolute uncertainty of each plotted value, and overlapping bars suggest the difference may not be meaningful.
Part 4 of 6Biology-Specific Diagrams
Dichotomous key
- Dichotomous key A branching key where each step offers two contrasting features that lead to a name or the next choice.
Food chain and web
- Food chain and web Arrows point from the organism eaten to the organism that eats it, showing the direction of energy flow.
Pyramid of energy
- Pyramid of energy Stacked bars drawn to scale show the energy available at each trophic level, which is always narrower higher up.
Pedigree chart
- Pedigree chart Squares are males and circles are females, and lines link parents to offspring to trace how a trait is inherited.
Part 5 of 6Worked Example
Question
- Oxygen from catalase breaking down hydrogen peroxide is collected in a gas syringe.
- A tangent drawn to the curve at t = 0 s passes through (0 s, 0 cm³) and (30 s, 12.6 cm³).
- Calculate the initial rate of reaction.
- Choose two widely separated points on the tangent, not on the curve: (0, 0) and (30, 12.6).
- Change in y = 12.6 cm³ − 0 cm³ = 12.6 cm³.
- Change in x = 30 s − 0 s = 30 s.
- Gradient = change in y ÷ change in x = 12.6 cm³ ÷ 30 s = 0.42 cm³ s⁻¹.
Answer The initial rate of reaction is 0.42 cm³ s⁻¹.
Part 6 of 6Exam Checklist & Tips
5.3.4 – Key Points for the Exam
- Independent variable The variable you change deliberately, always plotted on the x-axis.
- Tangent A straight line touching a curve at one point, whose gradient equals the rate at that point.
- Interpolation Estimating a value that lies between two plotted data points using the line of best fit.
- Extrapolation Extending a line of best fit beyond the plotted data to predict values, which is less reliable.
- Uncertainty bar A bar drawn through a plotted point to show the absolute uncertainty of that value.
Common Mistakes
- Joining points dot-to-dot instead of drawing a single smooth line or curve of best fit.
- Plotting the dependent variable on the x-axis, or leaving out the units in the axis labels.
- Taking a gradient from two points on the curve instead of two points on the tangent line.
- Using a bar chart for two continuous variables, or a line graph for separate categories.
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