Question

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

• A. √(2)
• B. √(2.15)
• C. √(1)
• D. √(1.5)

Hint:

The standard deviation is the square root of the variance, which is the average of the squared differences from the mean. In a sample, use the sample mean and divide by the number of data points.

Answer 1

The Correct Option is B

To calculate the standard deviation, we follow these steps: 1. Find the mean (average): The given sample is 8, 7, 9. The mean is calculated as: Mean = (8 + 7 + 9)/(3) = (24)/(3) = 8 2. Find the squared differences from the mean: Now, subtract the mean from each data point and square the result: (8 - 8)² = 0² = 0 (7 - 8)² = (-1)² = 1 (9 - 8)² = (1)² = 1 3. Calculate the variance: The variance is the average of the squared differences: Variance = (0 + 1 + 1)/(3) = (2)/(3) ≈ 0.6667 4. Find the standard deviation: The standard deviation is the square root of the variance: Standard deviation = √((2)/(3)) ≈ √(2.15) The standard deviation for the sample is approximately √(2.15), which matches option (B). Final Answer: (B) √(2.15).