Accuracy vs Precision: Percent Error and Sources of Uncertainty Worksheet

Question 1

A student measures the mass of a standard 50.0 g object three times and records 49.8 g, 50.1 g, and 50.0 g. Describe the accuracy and precision of the measurements.

Accepted Answer

The measurements are both accurate and precise. They are close to the accepted value of 50.0 g and close to one another.

Question 2

A thermometer reads 98.0 °C for boiling water when the accepted boiling point is 100.0 °C. Calculate the percent error.

Accepted Answer

The percent error is 2.0%. The calculation is |98.0 - 100.0| divided by 100.0 times 100, which equals 2.0%.

Question 3

Four students measure the length of the same table. Their results are 152.1 cm, 152.0 cm, 152.2 cm, and 152.1 cm. The true length is 155.0 cm. Are these measurements accurate, precise, both, or neither? Explain.

Accepted Answer

The measurements are precise but not accurate. They are very close to one another, but they are not close to the true length of 155.0 cm.

Question 4

A student finds the density of a metal sample to be 7.62 g/cm³. The accepted density is 7.87 g/cm³. Calculate the percent error to the nearest tenth of a percent.

Accepted Answer

The percent error is 3.2%. The calculation is |7.62 - 7.87| divided by 7.87 times 100, which equals about 3.2%.

Question 5

A group records the following times for one swing of a pendulum: 1.42 s, 1.41 s, 1.43 s, 1.42 s, and 1.41 s. The accepted period is 1.42 s. What do these data show about accuracy and precision?

Accepted Answer

The data show high accuracy and high precision. The measurements are tightly grouped and very close to the accepted value of 1.42 s.

Question 6

A balance has a resolution of 0.01 g. A student records a sample mass as 12.34 g. What is a reasonable uncertainty for this measurement, and how should the mass be written with uncertainty?

Accepted Answer

A reasonable uncertainty is plus or minus 0.01 g if using the instrument resolution. The mass can be written as 12.34 g ± 0.01 g.

Question 7

A graduated cylinder has markings every 1 mL. A student reads the bottom of the meniscus at 36.5 mL. Give one likely source of uncertainty and explain how it could affect the measurement.

Accepted Answer

One likely source of uncertainty is reading the meniscus from above or below eye level. This can cause parallax error, making the recorded volume too high or too low.

Question 8

An experiment gives these measured speeds for the same cart: 2.9 m/s, 3.4 m/s, 2.6 m/s, and 3.8 m/s. The accepted speed is 3.0 m/s. Describe the precision and explain what may have caused the pattern.

Accepted Answer

The measurements have low precision because they are spread far apart. The pattern may have been caused by inconsistent timing, different release points, friction changes, or reaction time errors.

Question 9

A student measures the acceleration due to gravity as 9.6 m/s². The accepted value is 9.8 m/s². Calculate the percent error.

Accepted Answer

The percent error is about 2.0%. The calculation is |9.6 - 9.8| divided by 9.8 times 100, which equals about 2.04%, so it rounds to 2.0%.

Question 10

A lab report states that a measured volume is 25.0 mL ± 0.5 mL. What is the range of possible values represented by this measurement?

Accepted Answer

The possible range is 24.5 mL to 25.5 mL. This comes from subtracting and adding 0.5 mL to the measured value of 25.0 mL.

Question 11

A class uses a stopwatch to measure how long a ball takes to fall. The times are consistently about 0.20 s longer than expected. Identify whether this is likely random error or systematic error, and explain.

Accepted Answer

This is likely systematic error because the measurements are consistently shifted in the same direction. A possible cause is reaction time delay when starting or stopping the stopwatch.

Question 12

In a target analogy, Group A has shots scattered widely around the bullseye. Group B has shots tightly clustered far from the bullseye. Compare the accuracy and precision of the two groups.

Accepted Answer

Group A may be somewhat accurate on average but has low precision because the shots are widely scattered. Group B has high precision but low accuracy because the shots are close together but far from the bullseye.

Question 13

A student reports a measured temperature as 21 °C using a thermometer marked every 1 °C. Another student reports 21.37 °C using the same thermometer. Which report is more appropriate, and why?

Accepted Answer

The report of 21 °C is more appropriate because the thermometer only has 1 °C markings. Reporting 21.37 °C suggests more precision than the instrument can provide.

Question 14

A graph of repeated mass measurements shows values clustered tightly near 18.0 g, while the accepted mass is 20.0 g. What conclusion should be made about the data, and what type of error might be present?

Accepted Answer

The data are precise but not accurate. A systematic error might be present, such as an incorrectly zeroed balance or calibration problem.

Question 15

A student calculates the percent error for a measured wavelength. The experimental value is 510 nm and the accepted value is 500 nm. The student writes -2.0% because 500 - 510 = -10. Explain the mistake and give the correct percent error.

Accepted Answer

The mistake is using a negative difference instead of the absolute difference. Percent error is reported as a positive value, so the correct percent error is |510 - 500| divided by 500 times 100, which equals 2.0%.

Accuracy vs Precision: Percent Error and Sources of Uncertainty

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