To answer the question, we need to evaluate the accuracy and precision of the given data set. Here are the steps:
1. Calculate the Mean (Average) of the Trials:
[tex]\[
\text{Mean} = \frac{\text{Sum of all trials}}{\text{Number of trials}} = \frac{58.7 + 59.3 + 60.0 + 58.9 + 59.2}{5} = 59.22
\][/tex]
2. Calculate the Standard Deviation of the Trials:
The standard deviation measures the amount of variation or dispersion in a set of values. The calculated standard deviation for the given trials is approximately [tex]\(0.4445\)[/tex].
3. Determine Accuracy:
Accuracy refers to how close the mean of the trials is to the correct value. We consider the data accurate if the mean is within a certain threshold of the correct value. Given that the mean is [tex]\(59.22\)[/tex] and the correct value is [tex]\(59.2\)[/tex], the difference is:
[tex]\[
|59.22 - 59.2| = 0.02
\][/tex]
Since [tex]\(0.02\)[/tex] is less than the accuracy threshold of [tex]\(0.5\)[/tex], the data set is considered accurate.
4. Determine Precision:
Precision refers to the consistency of the trials, which can be assessed using the standard deviation. A smaller standard deviation indicates greater precision. With a standard deviation of approximately [tex]\(0.4445\)[/tex], which is less than the precision threshold of [tex]\(0.5\)[/tex], we conclude that the data set is precise.
5. Final Description:
Since the data set is both accurate (mean is close to the correct value) and precise (small standard deviation), we describe the data set as:
"It is both accurate and precise."
