Drawing and Interpreting Graphs

Graph questions appear across all six papers in OCR Gateway Combined Science A. You may be asked to plot data, draw a line of best fit, read a value, calculate a gradient, or describe and explain a trend. These are dependable mark-earners if you follow the rules — and they are also questions where careless slips (wrong axis, joining the dots, freehand construction lines) throw away easy marks. Because graph skills are identical whether the data comes from biology, chemistry or physics, mastering them once serves you everywhere.

By the end of this lesson you should be able to plot a graph correctly, draw an appropriate line of best fit, read values accurately, calculate a gradient with the right units, and describe trends using data.

Graph work targets AO2 (plotting, reading and calculating a gradient) and AO3 (describing, interpreting and evaluating the trend the data shows).

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Plotting a Graph — The Rules

Step 1: The axes

Rule	Detail
Independent variable	Goes on the x-axis (horizontal)
Dependent variable	Goes on the y-axis (vertical)
Labels	Each axis needs a label and a unit, e.g. "Temperature (°C)"
Scale	Use a scale that fills at least half the grid, with sensible intervals (1, 2, 5, 10, 20, 50…)

Step 2: Plot the points

Use small, neat crosses (×), not dots, and check both coordinates for each point.

Step 3: The line of best fit

Data pattern	What to draw
Linear	A straight line of best fit with a ruler; it need not pass through every point
Curved	A smooth curve; do not join points with straight segments
Scattered	A line following the overall trend, with roughly equal points above and below

Exam Tip: Do not join the dots unless the question explicitly says so. A line of best fit shows the underlying trend; dot-to-dot lines reward scatter and noise instead.

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An Example Graph

The sketch below shows force–extension data for a spring, with a straight line of best fit through the origin. Reading and analysing a graph like this is a standard physics practical task.

The line is straight and passes through the origin, so force is directly proportional to extension — the relationship you would expect for a spring within its limit of proportionality.

Exam Tip: A straight line through the origin means "directly proportional". A straight line that does not pass through the origin still shows a linear relationship, but the two quantities are not proportional — an important distinction examiners test.

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Reading Values from a Graph

To read a value off a line:

1. Find the given value on one axis.
2. Draw a straight construction line (with a ruler) across to the plotted line.
3. Drop or draw a line to the other axis.
4. Read the value and include the correct unit.

Exam Tip: Always use a ruler for construction lines. Freehand lines lead to inaccurate readings and lost precision marks.

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Calculating the Gradient

The gradient of a straight line gives the rate of change, and it carries a physical meaning depending on the axes.

$\text{gradient} = \frac{\text{change in } y}{\text{change in } x}$gradient=change in xchange in y​

Method:

1. Pick two points on the line (not raw data points, unless they lie exactly on it), as far apart as possible for accuracy.
2. Draw a large right-angled triangle between them.
3. Read the rise (change in $y$y) and the run (change in $x$x).
4. Divide, and attach the correct units.

Worked gradient example

A distance–time graph for a moving trolley has a straight section. Two points on the line are $(2 \text{ s}, 10 \text{ m})$(2 s,10 m) and $(8 \text{ s}, 40 \text{ m})$(8 s,40 m).

$\text{change in } y = 40 - 10 = 30 \text{ m}$change in y=40−10=30 m

$\text{change in } x = 8 - 2 = 6 \text{ s}$change in x=8−2=6 s

$\text{gradient} = \frac{30}{6} = 5 \text{ m/s}$gradient=630​=5 m/s

Because the axes are distance and time, this gradient is the speed: the trolley moves at 5 m/s.

Exam Tip: Always state the unit of the gradient and, for full marks, its physical meaning — "gradient = 5 m/s, which is the speed" scores better than a bare "5". Choosing points far apart reduces the effect of small reading errors.

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What a Gradient (or Area) Means

The physical meaning of a graph depends entirely on its axes:

Axes ($y$y vs $x$x)	Gradient means	Area under means
distance vs time	speed	—
velocity vs time	acceleration	distance travelled
concentration vs time	rate of reaction	—
current vs voltage	1 ÷ resistance	—

flowchart TD
    A[Graph in the exam] --> B{What are the axes?}
    B -->|distance vs time| C[Gradient = speed]
    B -->|velocity vs time| D[Gradient = acceleration; area = distance]
    B -->|concentration vs time| E[Gradient = rate of reaction]
    B -->|current vs voltage| F[Gradient = 1 over resistance]

Exam Tip: For a curved graph you cannot use two points directly — draw a tangent to the curve at the point of interest and find the gradient of that tangent. This is how you read the rate at a specific time from a chemistry concentration–time curve.

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Describing Trends

When asked to "describe the trend", follow a three-part structure:

1. State the overall pattern — "As X increases, Y increases / decreases / stays the same."
2. Quote data — "The rate rises from 5 cm³/min at 20 °C to 15 cm³/min at 40 °C."
3. Note any change — "Above 40 °C the rate falls."

Quality	Answer
Poor	"The line goes up then down."
Good	"As temperature rises from 20 °C to 40 °C the rate increases from 5 to 15 cm³/min; above 40 °C the rate decreases, falling to 2 cm³/min at 60 °C."

Exam Tip: Always quote specific values when describing a trend. Vague descriptions without data cannot reach full marks — the numbers are the evidence the examiner is paying for.

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Correlation vs Causation

A common analysis question asks whether data show correlation, and whether that proves causation.

Term	Meaning
Positive correlation	As one variable increases, so does the other
Negative correlation	As one increases, the other decreases
No correlation	No pattern between the variables
Causation	One variable directly causes the change in the other

Exam Tip: A correlation does not prove causation — there may be a confounding variable. Ice cream sales and drowning rates rise together, but ice cream does not cause drowning; hot weather drives both.

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Anomalies