Chapter 2.3, Problem 51SSC

Interpretation Introduction

Interpretation:

The data is given for the number of coins and their masses. If the mass of a single coin is 5.00 g, the accuracy and precision of the given measurements need to be explained.

Concept introduction:

Accuracy is defined as how close is the measured value to its actual value. On the other hand, precision is a measure of the reproducibility of a set of measurements. Accuracy depends on the person measuring while the precision value depends on the measuring tool.

Answer to Problem 51SSC

If the masses of single coins are compared, the data is not accurate because the mass of a single coin vary and cannot be considered accurate. In addition, the data is not as precise as the mass of each coin is not within the accepted range.

Explanation of Solution

The given data is represented as follows:

Number of coins	5	10	20	30	50
Mass (g)	23.2	54.5	105.9	154.5	246.2

The mass of each coin can be calculated by dividing the total mass of the coin by the number of coins in each group in order to determine the precision and accuracy.

According to the data, for 5 coins mass is 23.2 thus, the mass of a single coin can be calculated by dividing two values. Thus, the mass of 1 coin will be:

$m=\frac{23.2}{5}=4.64\text{ g}$

Similarly, the mass of one coin for each measurement can be calculated as follows:

Number of coins	5	10	20	30	50
Mass (g)	23.2	54.5	105.9	154.5	246.2
Mass of 1 coin	4.64	5.45	5.295	5.15	4.924

By comparing the masses of single coins in each group, the data is not accurate. The value of the mass of a single coin varies too much to be considered accurate.

Moreover, the data is not as precise as the mass of each coin is not within the accepted range. The values must be close to 5 g which is given as accepted value for the mass of 1 coin.

Conclusion

Thus according to the given data, the measurement is not accurate and precise.