44
Reliability of Measurements
nearest 0.001 cm. Now the two results might be 1.792 cm and 1.796 cm. It
would now be proper to report the average value of 1.794 cm, because the third
decimal place is reasonably well known. It would be even more informative to
report the result as 1.794 ± 0.002 cm. The symbol ± is read as "plus or
minus." It shows that the actual results vary by 0.002 cm in either direction
from the reported average value.
In talking about the results of measurements, we distinguish between the
accuracy and the precision of the results. The accuracy of a series of measurements tells how closely the average of the results agrees with the true value of
the quantity that is measured. The precision of a series of measurements tells
how nearly the repeated measurements yield the same result. For example,
suppose that the markings on a centimeter scale are placed too far apart (as if
the scale has been stretched). In this case, the results obtained in a series of
measurements of the same object might be quite precise (different measurements would yield nearly the same answer), but they would be inaccurate (the
average result would be far from the true value).
Measurements commonly involve systematic errors. These are errors that are
reproducibly introduced in each measurement because of the construction, use,
or calibration of the equipment (as in the case of the stretched scale). The
precision of the results may give the illusion of accuracy in such cases. For this
reason, it is desirable to make a measurement by various entirely different
methods. If the results still show high precision (close agreement with one
another), then it is unlikely that systematic errors exist. The accuracy of the
measurement can also be tested by using the same measurement methods on a
"standard sample" whose value has been certified by some reliable institution,
such as the National Bureau of Standards.
Measurements also commonly involve random errors. These are errors whose
size and direction differ from measurement to measurement; that is, they are
unpredictable and unreproducible. They are commonly associated with the
limited sensitivity of instruments, the quality of the scales being read, the
degree of control over the environment (temperature, vibration, humidity, and
so on), or human frailties (limitations of eyesight, hearing, judgment, and so
on). We shall say much more about random error later in this chapter.
SIGNIFICANT FIGURES
All digits of a number that are reasonably reliable are known as significant
figures. The number 1.79 has three significant figures: 1, 7, and 9. The number
1.794 has four significant figures.
The position of the decimal point in a measured value has nothing to do with
the number of significant figures. The diameter of a dime may be given as 1.794
cm or as 17.94 mm. In either case, four significant figures are used.
Reliability of Measurements
nearest 0.001 cm. Now the two results might be 1.792 cm and 1.796 cm. It
would now be proper to report the average value of 1.794 cm, because the third
decimal place is reasonably well known. It would be even more informative to
report the result as 1.794 ± 0.002 cm. The symbol ± is read as "plus or
minus." It shows that the actual results vary by 0.002 cm in either direction
from the reported average value.
In talking about the results of measurements, we distinguish between the
accuracy and the precision of the results. The accuracy of a series of measurements tells how closely the average of the results agrees with the true value of
the quantity that is measured. The precision of a series of measurements tells
how nearly the repeated measurements yield the same result. For example,
suppose that the markings on a centimeter scale are placed too far apart (as if
the scale has been stretched). In this case, the results obtained in a series of
measurements of the same object might be quite precise (different measurements would yield nearly the same answer), but they would be inaccurate (the
average result would be far from the true value).
Measurements commonly involve systematic errors. These are errors that are
reproducibly introduced in each measurement because of the construction, use,
or calibration of the equipment (as in the case of the stretched scale). The
precision of the results may give the illusion of accuracy in such cases. For this
reason, it is desirable to make a measurement by various entirely different
methods. If the results still show high precision (close agreement with one
another), then it is unlikely that systematic errors exist. The accuracy of the
measurement can also be tested by using the same measurement methods on a
"standard sample" whose value has been certified by some reliable institution,
such as the National Bureau of Standards.
Measurements also commonly involve random errors. These are errors whose
size and direction differ from measurement to measurement; that is, they are
unpredictable and unreproducible. They are commonly associated with the
limited sensitivity of instruments, the quality of the scales being read, the
degree of control over the environment (temperature, vibration, humidity, and
so on), or human frailties (limitations of eyesight, hearing, judgment, and so
on). We shall say much more about random error later in this chapter.
SIGNIFICANT FIGURES
All digits of a number that are reasonably reliable are known as significant
figures. The number 1.79 has three significant figures: 1, 7, and 9. The number
1.794 has four significant figures.
The position of the decimal point in a measured value has nothing to do with
the number of significant figures. The diameter of a dime may be given as 1.794
cm or as 17.94 mm. In either case, four significant figures are used.