Errors, Accuracy & Precision

What are experimental errors?

Uncertainties associated with every measurement because all measurements are estimates.

Why is one measurement not enough to calculate error?

Error can only be calculated on the basis of a data set; a single measurement is insufficient.

Why do scientists need to understand errors?

To manage uncertainty and correctly interpret experimental results.

What is accuracy?

How close a set of measured values is to the true value.

What is precision?

How reproducible measurements are, regardless of closeness to the true value.

What does the “spread” of results describe?

The precision of the measurements.

What is a systematic (determinate) error?

A consistent, one-directional error that affects accuracy.

How does systematic error affect measurements?

Measurements are always too high or always too low.

Can systematic errors be corrected by averaging?

No, averaging repeated measurements does not remove systematic errors.

What are common causes of systematic errors?

Faulty instruments or incorrect procedures.

How can systematic errors be reduced or removed?

Through calibration, improved procedures, or better training.

What is a random (indeterminate) error?

An error caused by uncontrollable or hard-to-control variables.

How do random errors affect measurements?

They affect precision rather than accuracy.

Are random errors one-directional?

No, they are bi-directional with equal chance of being too high or too low (±).

How can random error be reduced?

By averaging repeated measurements.

Can random error be completely eliminated?

No, it can only be minimised.

Which type of error is treated mathematically?

Random errors.

How are systematic errors handled mathematically?

They are not; the source of the error must be identified and corrected.

What is meant by the limit to uncertainty?

The margin of error associated with a measurement.

What is absolute uncertainty?

The margin of uncertainty associated with a measurement.

Give an example of absolute uncertainty.

14.3 ± 0.1 cm.

What determines the magnitude of absolute uncertainty?

The measuring instrument, usually the smallest possible measurement it can make.

What units does absolute uncertainty have?

The same units as the measured value.

What is percentage (relative) uncertainty?

Absolute uncertainty expressed as a percentage of the measured value.

Give an example of percentage uncertainty.

14.3 cm ± 0.7%.

How do you convert absolute uncertainty to percentage uncertainty?

(Absolute uncertainty ÷ measured value) × 100.

How do you convert percentage uncertainty to absolute uncertainty?

(Percentage uncertainty ÷ 100) × measured value.

What is error propagation?

The way uncertainties carry through calculations involving measurements.

Why must error propagation be considered?

Calculations performed on measurements introduce additional uncertainty.

How do errors propagate when adding or subtracting quantities?

Absolute uncertainties are added.

What type of uncertainty must be used for addition and subtraction?

Absolute uncertainty.

How do errors propagate when multiplying or dividing quantities?

Percentage uncertainties are added.

What type of uncertainty must be used for multiplication and division?

Percentage (relative) uncertainty.

Why is BODMAS important in error propagation?

Because calculations must be done in the correct order.

What does BODMAS stand for?

Brackets, Orders (operations), Division/Multiplication, Addition/Subtraction.

What is often required when applying BODMAS to uncertainties?

Repeated conversion between absolute and percentage uncertainties.

What key ideas are covered in Topic 2: Experimental Errors?

• Accuracy

• Precision

• Uncertainty

• Systematic

• Random errors

• Absolute

• Percentage uncertainty

• Error propagation in calculations