# Create a set of data that meets the following criteria. A precise but not accurate determination of the mass of a can of Dr. Pepper that is 357.3 grams.

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### 1 Answer

To understand the answer to this question, one must understand the difference between measurements that are accurate and measurements that are precise.

Precision of measurement can be thought of as the repeatability of a measurement. That is, if the measurement of an object is repeated several times we can say it is a precise measurement if the values are all within a narrow range. Repeatability, or precision, can often times be linked to the quality (and subsequent cost) of the tool being used to make the measurement. For example, measuring length with a meter stick that is marked down to the nearest millimeter can be more precise than one that is marked down to the nearest centimeter; meter sticks calibrated to millimeters tend to be more expensive than those that are only at the centimeter range. Instruments with smaller degrees of calibration (mm vs. cm for example) generally have more digits in the recording of the correct measured quantity. Thus, the precision is also related to the number of significant digits used to report the value.

Accuracy and precision are often used synonymously in common speech. However, in scientific measurements they are not interchangeable concepts. Accuracy is how close a given measurement is to the correct, or true, value. For example, if a correct value of a measured length is 2.125 cm and you measure it to be 2.124 cm, you have made a pretty accurate measurement.

A good measurement is one which is both precise and accurate.

To create a set of data points that would represent a precise measurent of the mass of a can of soda pop which is not accurate we would expect measurement with a large number of significant digits, that are within a very narrow range, but which are not very close to the correct value of the mass of the can. An example set might look something like this:

The correct, or true, value: 357.3 g

Measurement 1: 525.3 g

Measurement 2: 525.1 g

Measurement 3: 525.2 g

All three measurements are close together (precise), but not very close to the correct value