Accuracy and Precision

Which of the following statements best describes precision?

• the closeness of a measurement to the true value

• the repeatability or consistency of a set of measurements

• the ability to measure small quantities

• the correctness of the measuring tool

Answer explanation

Precision refers to the repeatability or consistency of a set of measurements, indicating how closely multiple measurements of the same quantity agree with each other.

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NGSS.MS-PS3-4

A student measured the length of a table four times and got results of 1.00 m, 1.01 m, 1.00 m, and 1.01 m. The true length of the table is 1.50 m. How would you describe the student's measurements?

• both accurate and precise

• precise but not accurate

• accurate but not precise

• neither accurate nor precise

Answer explanation

The student's measurements are consistent (1.00 m and 1.01 m), indicating precision. However, they are not close to the true length of 1.50 m, indicating a lack of accuracy. Therefore, the measurements are precise but not accurate.

Which of the following would most likely improve the accuracy of a measurement?

• using a more precise instrument

• taking repeated measurements and averaging them

• calibrating the measuring instrument

• using a tool with smaller divisions

Answer explanation

Calibrating the measuring instrument ensures it provides accurate readings by correcting any systematic errors, thus improving measurement accuracy more effectively than other options.

In a factory, two machines are measuring the same object’s mass. Machine A consistently measures the mass as 50.05 kg, while Machine B measures it as 49.00 kg, 51.00 kg, and 50.00 kg. The true mass is 50.00 kg. Which machine is more precise?

• Machine A

• Machine B

• both machines are equally precise

• neither machine is precise

Answer explanation

Machine A is more precise because it consistently measures the mass as 50.05 kg, showing little variation. In contrast, Machine B's measurements vary significantly (49.00 kg to 51.00 kg), indicating less precision.

A team of scientists is measuring the boiling point of a liquid. Their data shows measurements of 98°C, 97.9°C, 98.1°C, and 98°C. The actual boiling point of the liquid is 100°C. Which statement best describes the data?

• high precision, low accuracy

• low precision, high accuracy

• high precision, high accuracy

• low precision, low accuracy

Answer explanation

The measurements (98°C, 97.9°C, 98.1°C, 98°C) are close to each other, indicating high precision. However, they are far from the actual boiling point of 100°C, indicating low accuracy. Thus, the correct description is high precision, low accuracy.

Which of the following best describes a measurement that is highly accurate?

• It is very close to the true value.

• It can be repeated many times with the same result.

• It has a small number of significant digits.

• It is the smallest possible reading.

Answer explanation

A measurement is considered highly accurate when it is very close to the true value. This indicates that the measurement reflects the actual quantity being measured, which is the essence of accuracy.

An engineer uses a caliper with a precision of 0.01 mm to measure the diameter of a pipe. Which of the following would be the most appropriate description of this precision?

• It improves the accuracy of the measurement.

• It ensures the measurement is closest to the true value.

• It increases the consistency of repeated measurements.

• It reduces systematic error.

Answer explanation

The precision of 0.01 mm allows for more consistent measurements when the engineer measures the pipe multiple times. This consistency is crucial for reliability in engineering applications.

A scale consistently measures a 100 g mass as 95 g. What type of error is the scale introducing?

• Random error, affecting precision.

• Systematic error, affecting accuracy.

• Random error, affecting ac.curacy

• Systematic error, affecting precision.

Answer explanation

The scale consistently measures a 100 g mass as 95 g, indicating a consistent offset. This is a systematic error, which affects accuracy because the measurements are consistently incorrect, rather than random fluctuations.

In an experiment, a scientist measures the speed of a toy car multiple times and obtains values that vary greatly. Which strategy would best improve the precision of the results?

• Use a more accurate stopwatch.

• Repeat the measurements under the same conditions.

• Use a more sensitive scale.

• Take only one careful measurement.

Answer explanation

Repeating the measurements under the same conditions helps to average out random errors and variability, leading to more consistent results and improved precision in the speed measurements of the toy car.

Which of the following instruments would provide the most precise measurement of the volume of a liquid?

• A beaker with 100 mL markings.

• A graduated cylinder with 1 mL markings.

• A flask with 50 mL markings.

• A measuring cup with 10 mL markings.

Answer explanation

A graduated cylinder with 1 mL markings provides the most precise measurement of liquid volume, as it allows for more accurate readings compared to the other options, which have larger increments.