Uncertainties in Scientific Measurements

All measurements are subject to error. To some extent, measuring instruments have built-in or inherent errors, called systematic errors. (For example, a kitchen scale might consistently yield results that are 25 g too high or a thermometer a reading that is 2°C too low.) Limitations in an experimenter’s skill or ability to read a scientific instrument also lead to errors and give results that may be either too high or too low. Such errors are called random errors.

Precision refers to the degree of reproducibility of a measured quantity that is, the closeness of agreement when the same quantity is measured several times. The precision of a series of measurements is high (or good) if each of a series of measurements deviates by only a small amount from the average. Conversely, if there is wide deviation among the measurements, the precision is poor (or low). Accuracy refers to how close a measured value is to the accepted, or actual value. High-precision measurements are not always accurate, a large systematic error could be present. (A tight cluster of three darts near the edge of a dart board can be considered precise but not very accurate if the intention was to strike the center of the board.) Still, scientists generally strive for high precision in measurements.

To illustrate these ideas, consider measuring the mass of an object by using the two balances shown in the figure. One of the balances is a single- pan balance that gives the mass in grams with only one decimal place. The other balance is a sophisticated analytical balance that gives the mass in grams with four decimal places. The accompanying table gives results obtained when the object is weighed three times on each balance. For the single-pan balance, the average of the measurements is 10.5 g, with measurements ranging from 10.4 g to 10.6 g. For the analytical balance, the average of the measurements is 10.4978 g, with measurements ranging from 10.4977 g to 10.4979 g. The scatter in the data obtained with the single- pan balance (±0.1 g) is greater than that obtained with the analytical balance (± 0.0001 g). Thus, the results obtained by using the single-pan balance have lower (or poorer) precision than those obtained by using the analytical balance.