When scientists need to compare the results of two different
measurements, the absolute
difference between the values is of very little use. The magnitude of error of being off by
10 cm depends on whether you are measuring the length of a piece of paper or the distance
from New Orleans to Houston. To express the magnitude of the error (or deviation) between
two measurements scientists invariably use percent error .
If you are comparing your value to an accepted value, you first
subtract the two values so
that the difference you get is a positive number. This is called taking the absolute value
of the difference. Then you divide this result (the difference) by the accepted value to
get a fraction, and then multiply by 100% to get the percent error.
So, % error = | your
result - accepted value | x 100 %
Several points should be noted when using this equation to obtain a percent error.
1) When you subtract note how
many significant figures remain
after the subtraction, and
express your final answer to no more than that number of digits.
2) If neither of the two values being compared is an
"accepted value", then use either
number in the denominator to get the fraction. If one value is more reliable than the
other, choose it for the denominator.
3) Treat the % symbol as a unit. The
fraction is dimensionless because units
in the values will cancel.
4) Notice that the error is a positive number
if the experimental value is too high, and is a
negative number if the experimental value is too low.
Example: A student measures the volume of a 2.50 liter
container to be 2.38 liters.
What is the percent error in the student's measurement?
Ans. % error
= (2.50 liters - 2.38 liters) x 100%
= (.12 liters) x
= .048 x 100%
= 4.8% error
(Note only two sig figs left in the answer after the subtraction)
Frequently in science, an accepted or true value is not known. The accuracy of a measurement cannot be reported if an accepted value is unavailable. Precision is a measure of how reproducible experimental measurements are. Precision is reported as Deviation or Difference of values.
The Absolute Deviation, or Absolute Difference, of each measurement is the difference of each measurement from the mean or average:
Absolute deviation = Measured value - Mean
The Average Deviation, or Average Difference, is the average of all of the absolute deviations. The Percent Deviation, or Percent Difference, is the average deviation reported as a percentage:
Deviation = Average Deviation x 100%