1.3.2 Precision and Accuracy

Question 1

Precision and Accuracy

Answer 1

• Any measurement will have a degree of uncertainty.
• Precision is the reproducibility of a measurement of a given quantity
• Accuracy is how close a measurement is to the true value.

Question 2

note

Answer 2

• Any measurement will have a degree of uncertainty.
• For example, a measurement of 166 pounds could actually be anywhere from 165 pounds to 167 pounds. This is often written as 166 ± 1 pound.
• Furthermore, if the scale isn’t calibrated correctly, the value of 166 pounds might not be correct.

Question 3

precision

Answer 3

• Precision is the reproducibility of a measurement of a given quantity. Precision reflects the uncertainty in the last digit of a measurement.
• Whenever a measurement is made, the last digit of the measurement must be estimated to one digit past the marking on the measuring device. This estimation leads to random error. Measurements with higher precision have less random error.
• For example, if the black bar is measured with a ruler marked in centimeters, the length is somewhere between 0 cm and 1 cm, but the tenths digit must be estimated. If the black bar is measured with a ruler marked in millimeters, the length is somewhere between 0.6 cm and 0.7 cm. In this case, the hundredths digit can be estimated, and the value is more precise.

Question 4

accuracy

Answer 4

• Accuracy is how close a measurement is to the true value. An analogy for this is a game of darts. The target is analogous to the true value. If three darts are thrown in a close grouping, but are nowhere near the target, they are precise, but not accurate.

Question 5

What are precise measurements?

Answer 5

• Precise measurements are all within a narrow range of values.

Question 6

During an experiment, you measure the following lengths for an object: 4.23 m, 4.21 m, 4.23 m, 4.22 m. Suppose that the actual, true length of the object is 5.02 m. Which statement best describes your measurements?

Answer 6

• Your measurements are not accurate but they are precise.

Question 7

Which of the following statements does NOT describe the scientific term precision?

Answer 7

• Precision reflects closeness to the “true” answer.

Question 8

What is the implied uncertainty in a measurement that reads 534.32 mg?

Answer 8

• ± 0.01 mg

Question 9

Suppose you are measuring heights of students. You have been using a measuring tape whose smallest unit is centimeters. Which of the following options would give you the greatest improvement in the precision of your readings?

Answer 9

• Use a measurement tape that has units of millimeters as its smallest unit.

Question 10

What is the difference between an experimental reading of 2 seconds and another reading (of the same event) of 2.0 seconds?

Answer 10

• The second reading (2.0 s) is more precise.

Question 11

Which of the following statements best describes the implied uncertainty of a measurement?

Answer 11

• Because any measurement device is limited by how small its units are, there is always an uncertainty in the last digit of a measurement.

Question 12

Suppose you measure the length of an object using a meter stick whose smallest indicated unit is a centimeter. The measurement you make is halfway between 10 and 11 centimeters. Which choice below best indicates the implied uncertainty of your measurement?

Answer 12

• ± 0.1 cm

Question 13

After being cited for speeding, you take your car to the shop to have the speedometer tested. They discover that all speeds are reported 10% lower than the true speed. What is this an example of?

Answer 13

• systematic error

- A systematic error always occurs in the same direction, as would be the case here.

Question 14

Suppose that during an experiment you record a weight measurement of 573.4 mg. Which digit in this reading is the implied uncertainty?

Answer 14

• 4