Step 1: Compute the Mean.
The sample mean (\( \bar{x} \)) is determined as follows:
\[\bar{x} = \frac{8 + 7 + 9}{3} = \frac{24}{3} = 8.\]
Step 2: Compute Squared Differences.
- For 8: \( (8 - 8)^2 = 0 \)
- For 7: \( (7 - 8)^2 = 1 \)
- For 9: \( (9 - 8)^2 = 1 \]
Step 3: Compute the Variance.
Variance (\( \sigma^2 \)) is the average of the squared differences:
\[\sigma^2 = \frac{0 + 1 + 1}{3} = \frac{2}{3}.\]
Step 4: Compute the Standard Deviation.
The standard deviation (\( \sigma \)) is the square root of the variance:
\[\sigma = \sqrt{\frac{2}{3}} \approx \sqrt{2}.\]
Step 5: Conclusion.
The calculated standard deviation is \( \sqrt{2} \), correlating to option (A).