Use the data set to answer the question.

\begin{tabular}{|l|l|}
\hline
\multicolumn{2}{|c|}{Correct Value: 59.2} \\
\hline
Trial 1 & 58.7 \\
\hline
Trial 2 & 59.3 \\
\hline
Trial 3 & 60.0 \\
\hline
Trial 4 & 58.9 \\
\hline
Trial 5 & 59.2 \\
\hline
\end{tabular}

Which best describes the data set?

A. It is accurate but not precise.
B. It is precise but not accurate.
C. It is both accurate and precise.
D. It is neither accurate nor precise.



Answer :

Let's analyze the given data set in detail.

1. Determine the Mean of the Trials:
First, we calculate the mean (average) of the given trials:
[tex]\[ \text{Mean} = \frac{\text{Trial 1} + \text{Trial 2} + \text{Trial 3} + \text{Trial 4} + \text{Trial 5}}{5} \][/tex]
Substituting in the given values:
[tex]\[ \text{Mean} = \frac{58.7 + 59.3 + 60.0 + 58.9 + 59.2}{5} = 59.22 \][/tex]

2. Determine the Standard Deviation of the Trials:
Next, we calculate the standard deviation, which measures the dispersion or variability of the trials:
[tex]\[ \sigma = \sqrt{\frac{\sum_{i=1}^{N} (x_i - \mu)^2}{N}} \][/tex]
Where [tex]\( N \)[/tex] is the number of trials, [tex]\( x_i \)[/tex] are the individual trial values, and [tex]\( \mu \)[/tex] is the mean.

After calculating the standard deviation using the given values, we get:
[tex]\[ \text{Standard Deviation} \approx 0.4445 \][/tex]

3. Assess Accuracy:
To determine accuracy, we check how close the mean of the trials is to the correct value (59.2). We use a threshold of [tex]\( \leq 0.5 \)[/tex]:
[tex]\[ \text{Accuracy} = \left| 59.2 - 59.22 \right| \leq 0.5 \][/tex]
[tex]\[ \text{Accuracy} = 0.02 \leq 0.5 \quad \text{(True)} \][/tex]

4. Assess Precision:
For precision, we check the standard deviation. A small standard deviation indicates high precision. Using a threshold of [tex]\( \leq 0.5 \)[/tex]:
[tex]\[ \text{Precision} = 0.4445 \leq 0.5 \quad \text{(True)} \][/tex]

Combining these assessments, we determine that the data set is both accurate and precise.

Therefore, the best description for the data set is:
- It is both accurate and precise.