Question

The standard deviation of 10, 16, 10, 16, 10, 10, 16, 16 is:

• A. 4
• B. 6
• C. 3
• D. 0

Hint:

If data consists of only two values $x$ and $y$ with equal frequency, $\sigma = \frac{|x-y|}{2}$.

Answer 1

The Correct Option is C

Step 1: Concept
Standard Deviation ($\sigma$).

Step 2: Analysis
Mean ($\mu$) = $(10+16+10+16+10+10+16+16) / 8 = 104 / 8 = 13$.

Step 3: Calculation
Variance ($\sigma^2$) = $\frac{\sum (x_i - \mu)^2}{N}$
$= \frac{4(10-13)^2 + 4(16-13)^2}{8} = \frac{4(-3)^2 + 4(3)^2}{8} = \frac{36+36}{8} = \frac{72}{8} = 9$.
$\sigma = \sqrt{9} = 3$.

Step 4: Conclusion
The standard deviation is 3. Final Answer: (C)