Read the incomplete statement.
The effect of a(n) __________ error can often be reduced by averaging multiple trials, but the effect of a(n) __________ error cannot be reduced by averaging multiple trials.
Which option correctly completes the statement?
absolute; relative
relative; absolute
random; systematic
systematic; random
To determine which option correctly completes the statement, we need to understand the meanings of the terms provided: absolute, relative, random, and systematic errors.
Absolute error refers to the difference between the measured value and the true value. It gives an indication of how far off the measured value is from the actual value.
Relative error, on the other hand, is the ratio of the absolute error to the true value. It provides a measure of how accurate the measurement is in relation to the true value.
Random error refers to the unpredictable and random fluctuations in measurements that occur naturally. It can result from various sources such as instrument limitations, environmental factors, or human error. Random errors cause a deviation from the true value in different directions and magnitudes.
Systematic error, in contrast, is a consistent and fixed deviation from the true value. It occurs due to inherent flaws or biases in the measurement process or equipment. Systematic errors tend to affect measurements in the same way consistently, leading to a consistent offset from the true value.
Given these definitions, we can conclude that the option "systematic; random" correctly completes the statement. A systematic error can often be reduced by averaging multiple trials because the average can help to cancel out the consistent bias. However, a random error cannot be reduced by averaging multiple trials because it is unpredictable and affects measurements differently each time.