Question

The standard deviation of the numbers \( -3, 0, 3, 8 \) is

• A. \( \frac{\sqrt{60}}{2} \)
• B. \( \frac{\sqrt{62}}{2} \)
• C. \( \frac{\sqrt{65}}{2} \)
• D. \( \frac{\sqrt{66}}{2} \)
• E. \( \frac{\sqrt{67}}{2} \)

Hint:

Always compute mean first, then deviations to find variance.

Answer 1

The Correct Option is D

Concept: \[ \sigma = \sqrt{\frac{1}{n}\sum (x_i - \mu)^2} \]

Step 1: Find mean.
\[ \mu = \frac{-3 + 0 + 3 + 8}{4} = 2 \]

Step 2: Compute variance.
\[ (-3-2)^2 + (0-2)^2 + (3-2)^2 + (8-2)^2 \] \[ = 25 + 4 + 1 + 36 = 66 \] \[ \sigma^2 = \frac{66}{4} \]

Step 3: Standard deviation.
\[ \sigma = \sqrt{\frac{66}{4}} = \frac{\sqrt{66}}{2} \]