Worksheet: Measurement Accuracy and Precision

In this worksheet, we will practice defining measurement accuracy and precision and explaining different types of measurement errors that affect them.

Q1:

The diagram shows a target board and four sets of hits on it, (A), (B), (C), and (D). The shots were all aimed at the bull’s-eye of the target.

Which set of hits is both accurate and precise?

  • A(A)
  • B(D)
  • C(B)
  • D(C)

Which set of hits is neither accurate nor precise?

  • A(D)
  • B(A)
  • C(C)
  • D(B)

Which set of hits is accurate but not precise?

  • A(B)
  • B(A)
  • C(D)
  • D(C)

Which set of hits is precise but not accurate?

  • A(C)
  • B(B)
  • C(A)
  • D(D)

Q2:

Which of the following statements most correctly describes how zero measurement errors affect the accuracy and the precision of measurements?

  • AZero errors decrease measurement accuracy.
  • BZero errors decrease both the accuracy and the precision of measurements.
  • CZero errors decrease measurement precision.
  • DZero errors do not affect measurement accuracy or measurement precision.

Q3:

Which of the following statements most correctly describes how systematic measurement errors affect the accuracy and the precision of measurements?

  • ASystematic errors decrease measurement precision.
  • BSystematic errors do not affect measurement accuracy or measurement precision.
  • CSystematic errors decrease both the accuracy and the precision of measurements.
  • DSystematic errors decrease measurement accuracy.

Q4:

Which of the following statements most correctly describes how random measurement errors affect the accuracy and the precision of measurements?

  • ARandom errors do not affect measurement accuracy or measurement precision.
  • BRandom errors decrease both the accuracy and the precision of measurements.
  • CRandom errors decrease measurement accuracy.
  • DRandom errors decrease measurement precision.

Q5:

Which of the following statements most correctly describes the meaning of the precision of measurements?

  • AThe more precise the measurement of a quantity is, the smaller the predictable change that can be made between the measured value and other measured values of the same quantity.
  • BThe more precise the measurement of a quantity is, the closer the measured value is to the actual value of the measured quantity.
  • CA precise measurement is more accurate than an accurate measurement.
  • DA precise measurement is made using a correct measurement method.

Q6:

Which of the following statements most correctly describes the meaning of the accuracy of measurements?

  • AThe more accurate the measurement of a quantity is, the closer the measured value is to the actual value of the measured quantity.
  • BAn accurate measurement has a value that is the same value when a quantity is repeatedly measured.
  • CAn accurate measurement is made using a correct measurement method.
  • DThe more accurate the measurement of a quantity is, the smaller the predictable change that can be made between the measured value and other measured values of the same quantity.

Q7:

Which of the following statements does not correctly describe the relationship between the precision of a set of measurements and the resolution of a measuring instrument that makes the measurements?

  • AThe resolution of a measuring instrument can be applied to single measurements of a value, but precision can only be applied to a set of measurements.
  • BThe resolution of a measuring instrument cannot be better than the precision of the measurements made by that instrument.
  • CThe precision of measurements is affected by uncontrolled experimental variables changing the values of the quantities being measured. The resolution of a measuring instrument is not affected by changes in the values of measured quantities.
  • DThe precision of measurements cannot be better than the resolution of the instrument that makes them.

Q8:

A kettle is used to increase the temperature of 0.25 L of water by 50C, and the time taken for the temperature to change is measured three times. The same kettle is used to increase the temperature of 0.45 L of water by 50C. Again, three measurements are made. The measured results are shown in the table. Which of the two sets of results is more precise?

Volume of Water (L) Time (s) Time (s) Time (s)
0.25 15.5 15.2 15.9
0.45 45.1 44.9 45.4
  • AThe measurements of the heating time of the 0.45 L volume of water are more precise.
  • BThe measurements of the heating time of both volumes of water are equally precise.
  • CThe measurements of the heating time of the 0.25 L volume of water are more precise.

Q9:

An experiment is made to measure the acceleration due to gravity on Earth. The results of the experiment are shown in the table. At least one of the following types of errors is indicated by the results. Select the appropriate error types.

Acceleration /ms Acceleration /ms Acceleration /ms Acceleration /ms Acceleration /ms
9.3 9.3 9.3 9.3 9.3

Possible error types:

  1. Systematic error
  2. Random error
  3. Zero error
  • Aa, b, and c
  • Bc
  • Cb and c
  • Da and b
  • Ea and c

Q10:

The air temperature throughout the day is being measured outdoors in a city using an electronic thermometer. The thermometer is in the shade on a sunny day. The following measurement errors can occur.

Error 1: Sunlight is reflected off windows of nearby buildings, and some of the windows that are open in particular positions at particular times reflect sunlight onto the thermometer.

Error 2: An electrical fault causes the thermometer to record all air temperatures around it as 2C higher than they actually are.

Error 3: An electrical fault causes the thermometer to record all air temperatures around it as half of the value that they actually are.

Error 4: The thermometer breaks completely such that it records no data.

Which of the errors is a systematic error?

  • AError 3
  • BError 1
  • CError 2
  • DError 4

Which of the errors is a random error?

  • AError 4
  • BError 2
  • CError 1
  • DError 3

Which of the errors is a zero error?

  • AError 1
  • BError 2
  • CError 4
  • DError 3

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