Collecting and processing data practice questions.

Two lengths, each measured as (10.0 ± 0.2) cm, are added together. What is the absolute uncertainty in the total length?

• 0.4 cm
• 0.2 cm
• 0.04 cm
• 2%

Answer: 0.4 cm

For a sum or difference the absolute uncertainties add: 0.2 + 0.2 = 0.4 cm. A classic error is to add percentage uncertainties instead, which applies to products, not sums.

A quantity is calculated from r³, where r has a percentage uncertainty of 2%. What is the percentage uncertainty in r³?

• 6%
• 2%
• 8%
• 0.67%

Answer: 6%

For a power, multiply the percentage uncertainty by the exponent: 3 × 2% = 6%. Forgetting to multiply by the power gives the common wrong answer of 2%.

A quantity is proportional to √x. The measured value of x has a percentage uncertainty of 4%. What is the percentage uncertainty in the quantity?

• 2%
• 4%
• 8%
• 16%

Answer: 2%

A square root is a power of one half, so multiply the percentage uncertainty by ½: 4% × ½ = 2%. Treating the root as if it left the uncertainty unchanged gives 4%.

For an object with uniform acceleration, a graph of velocity against time is a straight line. What does the y-intercept of this line represent?

• The initial velocity of the object
• The constant acceleration of the object
• The total displacement of the object
• The average speed over the motion

Answer: The initial velocity of the object

At t = 0 the velocity equals the intercept, so it is the initial velocity. The gradient (not the intercept) gives the acceleration, and the area under the line gives the displacement.

A balance reads 0.2 g when the pan is empty, so every mass recorded in an experiment is 0.2 g too high. Which statement classifies this error and gives the correct remedy?

• a systematic error; subtract 0.2 g from every reading
• a random error; take more readings and average them
• a systematic error; take more readings and average them
• a random error; subtract 0.2 g from every reading

Answer: a systematic error; subtract 0.2 g from every reading

A zero offset shifts every reading in the same direction by the same amount — the definition of a systematic error — and averaging cannot remove a shift that is present in every value. It is corrected, not reduced, by subtracting the offset or re-zeroing the instrument.

Five readings of a wire's diameter agree with one another to within 0.01 mm, but the micrometer used has an uncorrected zero error. The readings are best described as

• accurate but not precise
• both accurate and precise
• precise but not accurate
• neither precise nor accurate

Answer: precise but not accurate

Precision describes the spread of the readings (small here), accuracy their closeness to the true value (spoiled by the zero error). The two are independent — a tight cluster around the wrong value is the standard illustration.