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 #1: Precision vs. Accuracy

Example #1: Which of the 4 following images is not precise and not accurate?

Practice: 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?

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.

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

Explain the difference between random error and systematic error.

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.

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?

Three 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/cm3. The following table presents lead density data (g/cm3) collected by different groups of students. Determine which of the following groups have
a) the most precise data
b) the most accurate data

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

Precision and accuracy.How would the darts be positioned on the target for the case of "good accuracy, poor precision"?

Explain the difference between precision and accuracy.

Explain the difference between random error and systematic error.

Assume that you have two graduated cylinders, one with a capacity of 5 mL and the other with a capacity of 50 mL.
Which cylinder will give the more accurate measurement?

Two students determine the percentage of lead in a sample as a laboratory exercise. The true percentage is 22.52%. The students results for three determinations are as follows:
1. 22.52, 22.48, 22.54
2. 22.64, 22.58, 22.62Which set is more precise?

Indicate which of the following are exact numbers:(a) the mass of a paper clip(b) the surface area of a dime(c) the number of inches in a mile(d) the number of ounces in a pound, (e) the number of microseconds in a week (f) the number of pages in this book

Indicate which of the following are exact numbers:(a) the mass of a 32-oz can of coffee(b) the number of students in your chemistry class(c) the temperature of the surface of the sun(d) the mass of a postage stamp(e) the number of milliliters in a cubic meter of water(f) the average height of students in your school

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.

What is the difference between random error and systematic error?

The following dartboards illustrate the types of errors often seen when one measurement is repeated several times. The bull's-eye represents the "true value," and the darts represent the experimental measurements. Which board best represents each of the following seenaríos: (a) measurements both accurate and precise? [Section 1.5]

The three targets from a rifle range shown on the next page were produced by: (A) the instructor firing a newly acquired target rifle; (B) the instructor firing his personal target rifle; and (C) a student who has fired his target rifle only a few times. (a) Comment on the accuracy and precision for each of these three sets of results. [Section 1.5]

The percentage of water in an unknown hydrated salt is to be determined by weighing a sample of the salt, heating it to drive off the water, cooling to room temperature, and re-weighing. Which procedural mistake would result in determining a percentage of water that is too low?(A) I only(B) II only(C) both I and II(D) neither I nor II

You have water in each graduated cylinder shown:You then add both samples to a beaker. How would you write the number describing the total volume? What limits the precision of this number?

Consider the results of the archery contest shown in this figure.(a) Which archer is most precise?

Consider the results of the archery contest shown in this figure.(b) Which archer is most accurate?

Consider the results of the archery contest shown in this figure.(c) Who is both least precise and least accurate?

The following dartboards illustrate the types of errors often seen in measurements. The bull’s-eye represents the actual value, and the darts represent the data.Which experiments yield the same average result?

The following dartboards illustrate the types of errors often seen in measurements. The bull’s-eye represents the actual value, and the darts represent the data.Which experiment(s) display(s) high precision?

The following dartboards illustrate the types of errors often seen in measurements. The bull’s-eye represents the actual value, and the darts represent the data.Which experiment(s) display(s) high accuracy?

The following dartboards illustrate the types of errors often seen in measurements. The bull’s-eye represents the actual value, and the darts represent the data.Which experiment(s) show(s) a systematic error?

The three targets from a rifle range shown below were produced by: (A) the instructor firing a newly acquired target rifle; (B) the instructor firing his personal target rifle; and (C) a student who has fired his target rifle only a few times.Comment on the accuracy and precision for each of these three sets of results.

The three targets from a rifle range shown below were produced by: (A) the instructor firing a newly acquired target rifle; (B) the instructor firing his personal target rifle; and (C) a student who has fired his target rifle only a few times.For the A and C results in the future to look like the B results, what needs to happen?

Classify the following sets of measurements as accurate, precise, both, or neither.(a) Checking for consistency in the weight of chocolate chip cookies: 17.27 g, 13.05 g, 19.46 g, 16.92 g

Classify the following sets of measurements as accurate, precise, both, or neither.(b) Testing the volume of a batch of 25-mL pipettes: 27.02 mL, 26.99 mL, 26.97 mL, 27.01 mL

Classify the following sets of measurements as accurate, precise, both, or neither.(c) Determining the purity of gold: 99.9999%, 99.9998%, 99.9998%, 99.9999%

These organic solvents are used to clean compact discs:The chemist analyzing the cleaner calibrates her equipment and finds that the pipet is accurate to ±0.02 mL, and the balance is accurate to ±0.003 g. Is this equipment precise enough to distinguish between ethanol and isopropanol?

The chemist in Example R‑14 did some further experiments. She found that the pipet used to measure the volume of the cleaner is accurate to +0.03 cm3. The mass measurement is accurate to +0.002 g. Are these measurements sufficiently precise for the chemist to distinguish between isopropyl alcohol and ethanol?

A laboratory instructor gives a sample of amino-acid powder to each of four students, I, II, III, and IV, and they weigh the samples. The true value is 8.72 g. Their results for three trials are:I: 8.72 g, 8.74 g, 8.70 g II: 8.56 g, 8.77 g, 8.83 gIII: 8.50 g, 8.48 g, 8.51 g IV: 8.41 g, 8.72 g, 8.55 gCalculate the average mass from each set of data, and tell which set is the most accurate.

A laboratory instructor gives a sample of amino-acid powder to each of four students, I, II, III, and IV, and they weigh the samples. The true value is 8.72 g. Their results for three trials are:I: 8.72 g, 8.74 g, 8.70 g II: 8.56 g, 8.77 g, 8.83 gIII: 8.50 g, 8.48 g, 8.51 g IV: 8.41 g, 8.72 g, 8.55 gPrecision is a measure of the average of the deviations of each piece of data from the average value. Which set of data is the most precise? Is this set also the most accurate?

A laboratory instructor gives a sample of amino-acid powder to each of four students, I, II, III, and IV, and they weigh the samples. The true value is 8.72 g. Their results for three trials are:I: 8.72 g, 8.74 g, 8.70 g II: 8.56 g, 8.77 g, 8.83 gIII: 8.50 g, 8.48 g, 8.51 g IV: 8.41 g, 8.72 g, 8.55 gWhich set of data is both the most accurate and the most precise?

A laboratory instructor gives a sample of amino-acid powder to each of four students, I, II, III, and IV, and they weigh the samples. The true value is 8.72 g. Their results for three trials are:I: 8.72 g, 8.74 g, 8.70 g II: 8.56 g, 8.77 g, 8.83 gIII: 8.50 g, 8.48 g, 8.51 g IV: 8.41 g, 8.72 g, 8.55 gWhich set of data is both the least accurate and the least precise?

A 1.000 mL sample of acetone, a common solvent sometimes used as a paint remover, was placed in a small bottle whose mass was known to be 38.0015 g. The following values were obtained when the acetone-filled bottle was weighed: 38.7798 g, 38.7795 g, and 38.7801 g. How would you characterize the precision and accuracy of these measurements if the true mass of the acetone was 0.7791 g?