Question

Calculate the standard deviation for the following sample: 8, 7, and 9.

• A. \( \sqrt{2} \)
• B. \( \sqrt{2.15} \)
• C. \( \sqrt{1} \)
• D. \( \sqrt{1.5} \)

Hint:

Standard deviation is the square root of the variance, which measures the spread of data points from the mean.

Answer 1

The Correct Option is A

Step 1: Calculate the mean.
The mean (\( \bar{x} \)) of the sample is: \[ \bar{x} = \frac{8 + 7 + 9}{3} = \frac{24}{3} = 8. \]

Step 2: Calculate the squared differences.
- For 8: \( (8 - 8)^2 = 0 \) - For 7: \( (7 - 8)^2 = 1 \) - For 9: \( (9 - 8)^2 = 1 \)

Step 3: Calculate the variance.
Variance (\( \sigma^2 \)) is the average of the squared differences: \[ \sigma^2 = \frac{0 + 1 + 1}{3} = \frac{2}{3}. \]

Step 4: Calculate 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 correct standard deviation is \( \sqrt{2} \), so the answer is (A).