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Tables, Graphs, Uncertainty

Learn and apply Tables, Graphs, Uncertainty in the published Chemistry course sequence.

  • GCE A-Level H2 Chemistry 9476-2027
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Tables, Graphs and Uncertainty: Orientation

Data-handling marks are “free marks” if you follow the examiner rails: headings with units, sensible graphs, and uncertainty written in the correct language.

Use this with Paper 4 Skills: Planning, MMO, PDO, ACE and the Practical and QA (A Level) hub so method, data, and evaluation marks stay aligned.

Definitions (Must Know)

A. Accuracy

Accuracy is how close a measured value is to the true value (or accepted value).

B. Precision

Precision is how close repeated measurements are to each other (how much they scatter).

C. Reliability

Reliability is the consistency of measurements (often improved by repeats and a small spread).

D. Absolute uncertainty

Absolute uncertainty is the ± value in the same unit as the measurement (e.g. ±0.10 cm³).

E. Percentage uncertainty

The percentage uncertainty is: percentage uncertainty = (absolute uncertainty)/(measured value) × 100%

Detailed Explanations

A. Workflow: build a table that earns marks

  1. Decide your independent variable (IV) and dependent variable (DV).
  2. Make headings in the form quantity / unit.
  3. Keep decimal places consistent within a column (match the instrument resolution).
  4. Put repeats in separate columns (or rows), then add a mean (if required).

Mini example (headings):

  • Concentration of HCl(aq) / mol dm⁻³
  • Time for cross to disappear / s

Avoid:

  • putting units inside every cell (units belong in the heading)
  • mixed precision (e.g. 2.0, 2.13, 2.134 in the same column)

B. Workflow: draw a graph and read a gradient

  1. Put IV on the x-axis and DV on the y-axis.
  2. Label each axis with quantity and unit.
  3. Choose a scale that uses at least half the grid.
  4. Plot points accurately (small crosses).
  5. Draw one best-fit line/curve (not dot-to-dot).
  6. If asked for a gradient, choose two well-separated points on the best-fit line and include units.

Mini example (gradient sentence):

  • “Gradient = 0.82 cm³ s⁻¹ (from two points on the line of best fit).”

Example Calibration Graph: Absorbance vs Concentration

Example Calibration Graph: Absorbance vs Concentration. Measured points, Best-fit line plotted as Absorbance against Concentration.

Scroll across the graph to read all labels.

Example Calibration Graph: Absorbance vs Concentration. Measured points, Best-fit line plotted as Absorbance against Concentration.Example Calibration Graph: Absorbance vs Concentration. Measured points, Best-fit line plotted as Absorbance against Concentration.
Example only: plot points clearly, then draw one best-fit line/curve (not dot-to-dot). Use the best-fit line for gradients and readings.
Open full-size graph
View figure data
Values and uncertainty for Example Calibration Graph: Absorbance vs Concentration
SeriesConcentration (mol dm-3)Concentration uncertaintyAbsorbance (AU)Absorbance uncertainty
Measured points00
Measured points0.020.11
Measured points0.040.23
Measured points0.060.33
Measured points0.080.45
Measured points0.10.56
Best-fit line00
Best-fit line0.10.56

C. Workflow: write uncertainty correctly

  1. Take the uncertainty value from the question if given (use that).
  2. If not given, use instrument resolution rules (e.g. burette reading uncertainty per reading).
  3. Convert to percentage uncertainty when comparing or combining measurements.

Because a titre uses two burette readings, therefore its absolute uncertainty is the sum of the reading uncertainties.

Typical Uncertainty Values (Use the Question’s Value First)
  • burette reading: often ±0.05 cm³ per reading (titre uses two readings)
  • balance: usually ±(resolution) (e.g. ±0.01 g)
  • stopwatch: depends on reaction speed; use the value given if provided

Percentage Uncertainty vs Measured Volume (Fixed ±0.10 cm3)

Percentage Uncertainty vs Measured Volume (Fixed ±0.10 cm3). ±0.10 cm3 plotted as Percentage uncertainty against Measured volume.

Scroll across the graph to read all labels.

Percentage Uncertainty vs Measured Volume (Fixed ±0.10 cm3). ±0.10 cm3 plotted as Percentage uncertainty against Measured volume.Percentage Uncertainty vs Measured Volume (Fixed ±0.10 cm3). ±0.10 cm3 plotted as Percentage uncertainty against Measured volume.
If the absolute uncertainty is fixed, larger readings give smaller percentage uncertainty (one reason titration titres are often aimed at around 20–30 cm3).
Open full-size graph
View figure data
Values for Percentage Uncertainty vs Measured Volume (Fixed ±0.10 cm3)
Measured volume (cm3)±0.10 cm3
52
101
150.67
200.5
250.4
300.33

D. Combining uncertainties (simple approach)

  • For sums/differences: add absolute uncertainties.
  • For products/quotients: add percentage uncertainties.

Worked Examples

Modelled example 1

Find the Absolute Uncertainty in a Titre

Core

Problem

A titre is calculated from two burette readings. Each reading has an uncertainty of ±0.05 cm³. Find the absolute uncertainty in the titre.
Study the worked solution

  1. Identify the operation

    Method

    Write the titre as final reading minus initial reading.

    Reason

    A delivered volume depends on two separate burette readings.

    Working

    Vₜᵢₜᵣₑ = V_f-Vᵢ.

  2. Combine absolute uncertainties

    Method

    Add the two reading uncertainties.

    Reason

    For a difference, absolute uncertainties add rather than cancel.

    Working

    0.05 + 0.05 = ±0.10 cm³.

Guided practice 2

Convert Mass Uncertainty to a Percentage

About 5 min

Problem

A mass is measured as 1.24 g using a balance with resolution 0.01 g. Estimate the percentage uncertainty.

Try this before viewing the solution

Absolute uncertainty
Unit: %

Hints

Hint 1: fraction
Divide absolute uncertainty by the measured value.
Hint 2: percentage
Multiply the uncertainty fraction by 100%.
View solution step by step

  1. Use the balance resolution

    Method

    Take the absolute uncertainty as ±0.01 g.

    Reason

    The question supplies the resolution to use for this estimate.

    Working

    Δ m = 0.01 g.

  2. Form a percentage

    Method

    Divide by the measured mass and multiply by 100.

    Reason

    Percentage uncertainty expresses the uncertainty relative to the size of the measurement.

    Working

    0.01/1.24 × 100% = 0.81%.

Common misconception 3

Correct an Unreliable Gradient Method

Find and correct the mistake

Learner method

A learner joins experimental points dot-to-dot and calculates a gradient from two adjacent raw points. Explain why this is weak and state the correct method.

Try this before viewing the solution

Line to use
Gradient points

View solution step by step

  1. Represent the trend

    Method

    Draw one appropriate line or curve of best fit rather than connecting every fluctuation.

    Reason

    Scatter reflects experimental variation; dot-to-dot segments overinterpret it.

    Working

    Use all plotted evidence to judge the best fit.

  2. Construct a large triangle

    Method

    Choose two well-separated points on the best-fit line and calculate Δ y/Δ x with units.

    Reason

    A large change in each axis reduces the fractional effect of coordinate-reading uncertainty.

    Working

    Gradient points need not be original data points.

Examiner practice 4

Audit a Results Table

4 marks

Examination question

A results table labels one column “temperature”, puts “seconds” above another, records temperatures as 20, 25.0 and 30.00, and places three repeat times in one cell. State four presentation corrections. [4 marks]

Try this before viewing the solution

View solution step by step

  1. Correct headings

    2 marks

    Method

    Use headings in quantity/unit form: “temperature / °C” and “time / s”.

    Reason

    A heading must identify both the measured quantity and its unit without putting units in data cells.

    Working

    Temperature / °C; time / s.

  2. Correct data structure

    2 marks

    Method

    Use consistent decimal places within the temperature column and give each repeat its own column, followed by a mean column if required.

    Reason

    Precision should match the instrument, and separate repeats keep the evidence checkable.

    Working

    Trial 1 / s | Trial 2 / s | Trial 3 / s | Mean time / s.

Challenge 5

Find the Uncertainty in a Mass Loss

Minimal support

Uncertainty transfer

A reaction flask has mass 18.46 g before reaction and 18.11 g after reaction. Each balance reading has uncertainty ±0.01 g. Calculate the mass loss, its absolute uncertainty and its percentage uncertainty.

Try this before viewing the solution

Unit: g
Unit: g
Unit: %

Hints

Hint 1: difference
The mass loss is initial minus final mass.
Hint 2: two readings
Add absolute reading uncertainties before converting to a percentage of the mass loss.
View solution step by step

  1. Calculate the difference

    Method

    Subtract the final mass from the initial mass.

    Reason

    The escaping product accounts for the decrease in measured mass.

    Working

    18.46-18.11 = 0.35 g.

  2. Combine reading uncertainties

    Method

    Add the two balance-reading uncertainties.

    Reason

    The calculated difference depends on both measurements.

    Working

    Δ m = 0.01 + 0.01 = 0.02 g.

  3. Express relative uncertainty

    Method

    Divide the absolute uncertainty by the mass loss and multiply by 100.

    Reason

    The relevant measured result is the 0.35 g difference, not either flask mass.

    Working

    0.02/0.35 × 100% = 5.71%.

Mind Stretchers

Mind stretcher 1Extension

A student measures a gas volume as 24.6 cm³ with an absolute uncertainty of ±0.2 cm³. The time taken is 12.4 s with an absolute uncertainty of ±0.2 s. The student calculates the rate as V/t. Find the rate and the percentage uncertainty in the rate.

Show Hint

Use the uncertainty of the difference between two readings, then compare percentage rather than absolute uncertainty.

Show Answer

Mark scheme:

  • Rate = 24.6/12.4 = 1.98 cm³ s⁻¹ (3 s.f.).
  • Percentage uncertainty in V = 0.2/24.6 × 100% = 0.81%.
  • Percentage uncertainty in t = 0.2/12.4 × 100% = 1.61%.
  • For a quotient, add percentage uncertainties: 0.81 + 1.61 = 2.42%.

Mind stretcher 2: Choosing the more precise experimental designExtension

Question. Method A uses two burette readings to obtain 5.00 cm³; Method B uses the same burette to obtain 25.00 cm³. Each reading has uncertainty ±0.05 cm³. Compare the percentage uncertainty in the delivered volumes and recommend a method.

Show Hint

Use the uncertainty of the difference between two readings, then compare percentage rather than absolute uncertainty.

Show Answer

A delivered volume uses two readings, so its absolute uncertainty is ±0.10 cm³. Method A has 0.10/5.00 × 100 = 2.0% uncertainty; Method B has 0.10/25.00 × 100 = 0.40%. Method B is more precise because the same absolute reading uncertainty is a smaller fraction of the measured volume.