Within every calculation made there is a level of error. Tied to this notion of error are the two major principles of precision and accuracy.
Concept: Precision vs. Accuracy
3mI know that there's a negative connotation attached to this word, errors, mistakes. We hate that. We always try our best to be as accurate as possible with all of our calculations in chemistry, but we need to realize that no matter what we do, there's always going to be a level of uncertainty attached with any calculation that we do. We're going to say that this level of uncertainty is called experimental error.
We're going to say when we investigate the quality of any experimental decision or calculation, we have to take into account to major categories. The first category deals with the reproducibility of our calculations.
Now ,what exactly does this mean? Well, this means that if I run an experiment and I do all the calculations and I get a number, if I do that experiment five more times, several more times, my answers each of the other times should be close to that first number. This is what we talk about reproducibility. All of our calculations, even though we do it several times, should give us around the same number. We're going to say that this is called precision. So our calculations can be precise, meaning all the results are going to be around the same number.
Common example for this is a dart board. We shoot out three darts and they all land in the basic same area. We're going to say our dart throwing will be very precise because every time we expect it to land around the same area.
Now, the second category that we're going to deal with, deals with how close we are to the actual value. So basically, when we look at this dart board, our actual value can be understood as the bull's eye. That's where we want to aim our dart. That's where we want to hit. If we hit the bull's eye, we're going to say that our throwing is very accurate. So we're going to say accuracy deals with how close we are to the measured value.
For example, we run an experiment. Our professor tells us we need to get an answer of 10. Let's say I do this experiment myself and I get an answer of 9.98. That's extremely close to 10, so I would say that my result is pretty precise. It's not perfectly precise and accurate, but it's pretty good. We're going to say that our 9.98 is actually accurate, pretty accurate. Close to 10.
So precision deals with the reproducibility of our calculations. Doing it more than once and our results being very close to one another. Accuracy means that I will be very close to my actual value. On the first example with the dart board, our three darts were very precise, but they weren't that accurate because we missed the bull's eye.
Example: Which of the 4 following images is not precise and not accurate?
1mProblem: A student must measure the weight of a sodium bicarbonate compound, NaHCO_{3}, and obtains the following measurements: 23.12 g, 23.08 g and 23.17g. If the true weight of the compound is 18.01 g what can be said about the student’s results?
2mThree groups of students measure the mass of a product from the same chemical reaction. The groups recorded data of 8.83 g, 8.84 g, and 8.82 g. The known mass of the produce from the reaction is 8.60 g. The groups values are ____.
a) Accurate
b) Precise
c) Accurate and precise
d) Neither accurate nor precise
The density of lead is 11.3 g/cm^{3}. The following table presents lead density data (g/cm^{3}) collected by different groups of students. Determine which of the following groups have
a) the most precise data
b) the most accurate data
Precision is the measure of
a) how close a measurement is to the “true” value
b) an object’s kinetic energy
c) how well repeated measurements agree with each other
d) the error inherent in every measurement
Which of the following is NOT an exact number?
A) Your weight in pounds.
B) The amount of pennies per dollar.
C) The number of milligrams in a kilogram.
D) The number students in this classroom.
Explain the difference between random error and systematic error.
Two electric balances are tested using a standard weight. The true mass of the standard is 1.3111 g. The results of the 5 individual measurements on each balance are recorded below.
Average mass =
Which statement best describes the results?
a) A: poor precision, good accuracy
b) B: good precision, poor accuracy
c) B: good precision, good accuracy
d) B: poor precision, poor accuracy
e) A: good precision, good accuracy
Winnie the Pooh set out to help Rabbit count his carrots. However, Pooh has trouble counting and always leaves out the numbers 8, 9, and 10. The count that Pooh got for the various piles was 46, 39, 6, 18, and 11. The count that Rabbit (whose counting is always perfect) got for the same piles was 43, 36, 6, 15, and 8, respectively. Rabbit was very angry at Pooh. What can be said about Pooh’s results?
a) They are accurate but not precise
b) They are precise but not accurate
c) They are accurate and precise
d) They are neither accurate nor precise
e) Not enough information is given to make a decision about accuracy and precision.
Consider the data obtained for the length of an object as measured by three students. The length is known to be 14.49350 cm. Which student has done the most accurate determination?
A chemist makes several measurements of the electrical conductivity of an unknown sample. With this information the chemist can discuss
A. The accuracy of the measurements.
B. The precision of the measurements.
C. Whether a determinate error is present.
D. The percentage error.