To determine the best description for the given experimental data, we need to evaluate two main aspects: accuracy and reproducibility. Here’s the step-by-step solution:
1. List the given data and the correct value:
- Correct value: [tex]\( 23.0 \)[/tex]
- Experiment values: [tex]\( 17.8, 18.0, 17.9, 18.2 \)[/tex]
2. Calculate the mean (average) of the experiment values:
[tex]\[
\text{Mean} = \frac{17.8 + 18.0 + 17.9 + 18.2}{4} = 17.975
\][/tex]
3. Determine Accuracy:
- Accuracy is judged by how close the mean of the experiment values is to the correct value.
- The mean is [tex]\( 17.975 \)[/tex], and the correct value is [tex]\( 23.0 \)[/tex].
- Since [tex]\( 17.975 \)[/tex] is more than 5 units away from [tex]\( 23.0 \)[/tex], the experiments are not accurate.
4. Determine Reproducibility (Precision):
- Reproducibility can be assessed by calculating the standard deviation of the experiments.
- The standard deviation of the experiment values is [tex]\( 0.1479 \)[/tex]. Given a low standard deviation, the experiment results are closely clustered around the mean, indicating that the experiments are reproducible.
5. Conclusion:
- Based on the steps above, the mean indicates that the experiments are not close to the correct value, making them not accurate.
- The low standard deviation suggests that the experiments are reproducible.
So, the best description for the data is:
"They are precise and reproducible."
