Question

The variance for the following discrete frequency distribution is

• A. 3
• B. 2
• C. 1
• D. 5 \bigskip

Hint:

Use \(\sigma^2=E(X^2)-[E(X)]^2\) for fast computation.

Answer 1

The Correct Option is B

Concept: Variance is given by: \[ \sigma^2=\frac{\sum f x^2}{N}-\left(\frac{\sum f x}{N}\right)^2 \]

Step 1: Compute mean and second moment.
After substituting values from the given distribution: \[ \bar{x}=4,\quad \frac{\sum fx^2}{N}=18 \]

Step 2: Compute variance.
\[ \sigma^2=18-16=2 \] \[ \boxed{(B)} \]