Four of your classmates measured the same volume

To describe the measurements of your classmates in terms of accuracy and precision, let's first take a look at the table provided. The table shows the results of three trials for each of the four classmates who measured the same volume of water. Here's the table:
$\begin{array}{cccc}\hfill \text{Classmate}\hfill & \hfill \text{Trial 1 (mL)}\hfill & \hfill \text{Trial 2 (mL)}\hfill & \hfill \text{Trial 3 (mL)}\hfill \\ \hfill \text{Classmate 1}\hfill & \hfill 4.20\hfill & \hfill 4.18\hfill & \hfill 4.19\hfill \\ \hfill \text{Classmate 2}\hfill & \hfill 4.26\hfill & \hfill 4.25\hfill & \hfill 4.23\hfill \\ \hfill \text{Classmate 3}\hfill & \hfill 4.21\hfill & \hfill 4.20\hfill & \hfill 4.19\hfill \\ \hfill \text{Classmate 4}\hfill & \hfill 4.22\hfill & \hfill 4.23\hfill & \hfill 4.24\hfill \end{array}$
Accuracy refers to how close the measured values are to the accepted value, which in this case is 4.25 mL. To assess accuracy, we can calculate the average of the measurements made by each classmate and compare it to the accepted value.
Let's calculate the average for each classmate:
For Classmate 1:
Average = ${\displaystyle \frac{4.20+4.18+4.19}{3}}=4.19$ mL
For Classmate 2:
Average = ${\displaystyle \frac{4.26+4.25+4.23}{3}}=4.25$ mL
For Classmate 3:
Average = ${\displaystyle \frac{4.21+4.20+4.19}{3}}=4.20$ mL
For Classmate 4:
Average = ${\displaystyle \frac{4.22+4.23+4.24}{3}}=4.23$ mL
Now, let's evaluate the accuracy of each classmate's measurements by comparing their average to the accepted value:
- Classmate 1: The average of their measurements (4.19 mL) is slightly lower than the accepted value (4.25 mL). Therefore, we can say their measurements are slightly less accurate.
- Classmate 2: The average of their measurements (4.25 mL) is equal to the accepted value (4.25 mL). Hence, we can say their measurements are accurate.
- Classmate 3: The average of their measurements (4.20 mL) is slightly lower than the accepted value (4.25 mL). Thus, we can say their measurements are slightly less accurate.
- Classmate 4: The average of their measurements (4.23 mL) is slightly higher than the accepted value (4.25 mL). Hence, we can say their measurements are slightly less accurate.
Precision, on the other hand, refers to the consistency or reproducibility of the measurements. It tells us how close the measured values are to each other. To assess precision, we can examine the range or the spread of the measurements for each classmate.
Let's calculate the range for each classmate:
For Classmate 1:
Range = Maximum value - Minimum value = $4.20-4.18=0.02$ mL
For Classmate 2:
Range = Maximum value - Minimum value = $4.26-4.23<br>=0.03$ mL
For Classmate 3:
Range = Maximum value - Minimum value = $4.21-4.19=0.02$ mL
For Classmate 4:
Range = Maximum value - Minimum value = $4.24-4.22=0.02$ mL
By examining the ranges, we can determine the precision of each classmate's measurements:
- Classmate 1: The range of their measurements (0.02 mL) indicates a high level of precision since the values are very close to each other.
- Classmate 2: The range of their measurements (0.03 mL) suggests a slightly lower precision compared to Classmate 1 since the values have a slightly larger spread.
- Classmate 3: The range of their measurements (0.02 mL) indicates a high level of precision similar to Classmate 1.
- Classmate 4: The range of their measurements (0.02 mL) also indicates a high level of precision similar to Classmate 1 and Classmate 3.