Paper 6 Tables and Graphs: Record, Plot and Interpret

Paper 6 tables and graphs reward disciplined recording. A correct trend can still lose marks through missing units, inconsistent precision, an unsuitable scale, tiny plotting or a gradient calculated from the wrong points.

The workflow is:

1. design or complete the table
2. record values consistently
3. choose axes and scale
4. plot accurately
5. draw the appropriate best-fit line or curve
6. calculate or interpret
7. identify anomalies and limitations

Designing a results table

A complete table needs:

• one heading for each variable
• units in the headings
• values arranged logically
• consistent precision within a measured column
• enough space for all readings and repeats

Use a heading format such as:

concentration / mol dm⁻³	time / s	rate / s⁻¹

Do not write “concentration” without a unit when the values are numerical. Do not repeat “s” after every time value when it is already in the heading.

Independent and dependent variables in a table

The independent variable normally appears in the first column. The measured dependent variable follows. Processed values such as mean or rate come after the raw readings.

For repeated measurements:

temperature / °C	time 1 / s	time 2 / s	time 3 / s	mean time / s

If one result is anomalous, mark it clearly and calculate the mean from the concordant values only, explaining the exclusion.

Precision and decimal places

Record measurements to the precision allowed by the apparatus.

Examples:

• burette readings are normally recorded consistently to two decimal places when the scale permits reading to the nearest 0.05 cm³
• a thermometer marked in whole degrees should not produce a reading such as 22.347°C
• balance readings should retain the displayed decimal places
• repeated readings in one column should use consistent decimal places

Precision is not improved by inventing extra digits.

Raw data versus processed data

Keep the original reading separate from calculations.

Raw data:

• initial mass
• final mass
• temperature at each time
• gas volume at each time

Processed data:

• mass loss
• temperature change
• mean
• rate
• gradient
• percentage

A table should make it clear which values were measured and which were calculated.

Choosing graph axes

The independent variable normally goes on the x-axis. The dependent variable goes on the y-axis.

Examples:

• time on x, gas volume on y
• concentration on x, rate on y
• temperature on x, solubility on y

Label each axis with the variable and unit.

Weak:

time

Better:

time / s

Choosing a scale

A good scale:

• uses more than half of the available grid in both directions
• has equal numerical intervals for equal distances
• is easy to read and plot
• covers all data without compressing points into one corner

Simple scales such as 1, 2, 5 or 10 units per major square are safer than awkward intervals such as 3 or 7 unless the data require them.

The axis does not always need to begin at zero, but a broken or truncated scale must not mislead and must follow the instructions and grid provided.

Plotting points

Use small, precise crosses or another permitted plotting symbol. The centre of the mark should show the coordinate.

Check each point by reading:

1. x-value
2. y-value
3. scale subdivisions
4. unit

Large blobs make accuracy impossible to judge.

Line or curve of best fit

Do not automatically join points dot to dot.

Use a straight line of best fit when the data show an approximately linear relationship. The line should balance the points rather than pass through the first and last point at all costs.

Use a smooth curve when the trend is curved, such as gas volume increasing and then approaching a maximum.

A best-fit line or curve represents the overall relationship and reduces the influence of random variation.

Anomalies

An anomalous result does not fit the pattern shown by the other data.

A complete response can:

• identify the coordinate or result
• state why it is anomalous relative to the trend
• exclude it from the best-fit line or mean where justified
• suggest repeating that measurement

Do not label a point anomalous merely because it is the highest or lowest value. It must depart unexpectedly from the pattern.

Original worked data set

A student measures the volume of gas produced by a reaction.

time / s	gas volume / cm³
0	0
20	18
40	32
60	43
80	51
100	56
120	59

Expected graph

• x-axis: time / s
• y-axis: gas volume / cm³
• smooth curve through or close to the points
• steep initial gradient
• decreasing gradient as reactants are used up
• curve approaching a maximum near 60 cm³

Description

The gas volume increases rapidly at first, then increases more slowly and approaches a constant final volume.

Explanation

The rate decreases because reactant particles are used up, so their concentration falls and successful collisions occur less frequently.

The description reports the graph. The explanation supplies the chemical cause.

Calculating a gradient

For a straight line:

gradient = change in y ÷ change in x

Use two well-separated points on the best-fit line. A larger triangle reduces the percentage uncertainty in reading the coordinates.

Example: a best-fit line passes through (20 s, 10 cm³) and (100 s, 50 cm³).

gradient = (50 − 10) cm³ ÷ (100 − 20) s
gradient = 40 ÷ 80 = 0.50 cm³ s⁻¹

Include the gradient unit.

Tangent gradients for curves

When the question asks for the rate at a particular time on a curved graph:

1. draw a tangent touching the curve at that time
2. choose two well-separated points on the tangent
3. calculate change in y divided by change in x
4. include units

Do not use two points on the curve far away from the required time; that gives an average rate over an interval, not the instantaneous rate represented by the tangent.

Interpolation and extrapolation

Interpolation estimates within the measured range. It is generally more reliable because it lies between experimental points.

Extrapolation estimates beyond the measured range. It is less secure because the relationship may change outside the observed data.

A good evaluation states this reason rather than merely calling extrapolation “bad”.

Drawing conclusions from graphs

A conclusion should match the evidence and avoid claiming more than the data show.

Weak:

Higher concentration is better.

Better:

Within the tested range, increasing hydrochloric acid concentration increases the initial rate, shown by the increasing gradient of the gas-volume curves.

The phrase “within the tested range” prevents an unsupported claim about all possible concentrations.

Common table mistakes

1. Missing units in headings.
2. Units repeated in every cell.
3. Independent and dependent variables mixed without clear headings.
4. Inconsistent decimal places in the same measured column.
5. A mean calculated from an unexplained anomaly.
6. Raw and processed values combined without labels.
7. Missing repeat columns when the plan requires repeats.

Common graph mistakes

1. Axes reversed.
2. Axes missing units.
3. Scale occupying only a small part of the grid.
4. Unequal numerical intervals for equal distances.
5. Large, imprecise plotting marks.
6. Points joined dot to dot without considering the relationship.
7. An anomalous point forced into the best-fit line.
8. Gradient calculated from one tiny triangle or from data points not on the best-fit line.
9. Missing gradient units.
10. A description used where an explanation was required.

Final checklist

Table

• variables named
• units in headings
• consistent precision
• repeats visible
• mean or processed quantity labelled
• anomaly handled transparently

Graph

• independent variable on x-axis
• dependent variable on y-axis
• labels and units
• sensible scale
• precise points
• appropriate line or curve
• anomaly identified
• gradient triangle large and on the correct line
• units included

Continue with planning investigations and errors and improvements, then use the main Paper 6 guide as the component overview.