To determine which description best applies to the data set, we need to check both the accuracy and the precision of the measurements.
Steps to determine accuracy and precision:
1. Calculate the Mean:
First, we find the average (mean) of the trials.
[tex]\[
\text{Mean} = \frac{\text{Trial 1} + \text{Trial 2} + \text{Trial 3} + \text{Trial 4} + \text{Trial 5}}{5} = \frac{58.7 + 59.3 + 60.0 + 58.9 + 59.2}{5} = 59.22
\][/tex]
2. Calculate the Standard Deviation:
Next, we calculate the standard deviation to measure the precision of the trials. The standard deviation indicates how spread out the values are from the mean.
[tex]\[
\text{Standard Deviation} \approx 0.445
\][/tex]
3. Evaluate Accuracy:
Accuracy determines how close the mean of our trials is to the correct value. If the mean is within an acceptable range (threshold) of the correct value, it is considered accurate.
[tex]\[
\text{Correct Value} = 59.2
\][/tex]
The mean of 59.22 is very close to the correct value, within the threshold of 0.5 units, so it is accurate.
4. Evaluate Precision:
Precision assesses how consistent the measurements are with each other, indicated by a small standard deviation. A standard deviation below a defined threshold (say 0.5) signifies high precision.
[tex]\[
\text{Standard Deviation} \approx 0.445
\][/tex]
Since the standard deviation is below 0.5, the measurements are precise.
Combining these results, we find that:
- The data set is accurate because the mean of the measurements (59.22) is close to the correct value (59.2).
- The data set is precise because the standard deviation (0.445) is small, indicating that the measurements are consistent with each other.
Therefore, the best description of the data set is:
It is both accurate and precise.
