Answer: Sample Mean = 34.53, Standard deviation = 82.96

**Calculation Steps:** 1. **Sample Mean:** $$ \bar{X} = \frac{1}{n} \sum_{i=1}^{n} X_i = \frac{1}{100} \times 3,453 = 34.53 $$ 2. **Sample Variance:** $$ s^2 = \frac{1}{n-1} \left\{ \sum_{i=1}^{n} X_i^2 - n \bar{X}^2 \right\} = \frac{1}{99} (800,536 - 100 \times 34.53^2) $$ First calculate $34.53^2 = 1192.3209$ Then $100 \times 1192.3209 = 119,232.09$ So $800,536 - 119,232.09 = 681,303.91$ Finally $s^2 = \frac{681,303.91}{99} = 6,881.857677$ 3. **Sample Standard Deviation:** $$ s = \sqrt{6,881.857677} = 82.96 $$ **Verification:** - Sample mean = 34.53 ✓ - Standard deviation = 82.96 ✓ Therefore, option B is correct.

Author: Nikitesh Somanthe