To solve the problem and find the standard deviation, let's calculate step-by-step.

Given data values:

10, 20, 12, 17, and 16.

Step 1: Find the mean

The mean is the average of the values:

$\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$

$\text{Mean} = \frac{10 + 20 + 12 + 17 + 16}{5} = \frac{75}{5} = 15$

Step 2: Compute the squared differences from the mean

For each data value, calculate the squared difference from the mean:

• $(10 - 15)^2 = (-5)^2 = 25$
• $(20 - 15)^2 = (5)^2 = 25$
• $(12 - 15)^2 = (-3)^2 = 9$
• $(17 - 15)^2 = (2)^2 = 4$
• $(16 - 15)^2 = (1)^2 = 1$

Step 3: Calculate the variance

The variance is the average of these squared differences:

$\text{Variance} = \frac{\text{Sum of squared differences}}{\text{Number of values}}$

$\text{Variance} = \frac{25 + 25 + 9 + 4 + 1}{5} = \frac{64}{5} = 12.8$

Step 4: Compute the standard deviation

The standard deviation is the square root of the variance:

$\text{Standard deviation} = \sqrt{\text{Variance}} = \sqrt{12.8} \approx 3.58$

Thus, the standard deviation is approximately 3.58, which is not listed as an option in the given choices.

It seems there might be an error in either the question options or the interpretation of the computation method. Let me know if you'd like me to recheck or further explain this!

Would you like more details or have any questions?

Here are some related questions:

1. How is variance different from standard deviation?
2. Why is standard deviation useful in statistics?
3. How does sample size affect standard deviation?
4. What is the relationship between mean and variance?
5. How are deviations calculated for grouped data?

Tip: Always recheck whether a question specifies if it uses a population or sample formula for standard deviation.