A sample of $n=5$ scores has a mean of $m=20$ and a sample variance of $s^2=4$. What is the sample standard deviation?

• A. $s=16$
• B. $s=4$
• C. $s=2$
• D. $s=1$

Answer: (C)

Verified step by step guidance

1. Recall that the sample variance \(s^2\) is the square of the sample standard deviation \(s\). This means the relationship between them is given by the formula: \(s = \sqrt{s^2}\).
2. Identify the given sample variance from the problem, which is \(s^2 = 4\).
3. Apply the formula by taking the square root of the sample variance: \(s = \sqrt{4}\).
4. Calculate the square root to find the sample standard deviation, remembering that standard deviation is always non-negative.
5. Conclude that the sample standard deviation \(s\) is the positive square root of the variance, which completes the solution.