Answer: Sample Mean = 34.53, Standard deviation = 82.96

## Calculation Explanation ### Sample Mean Calculation The sample mean is calculated as: $$ \hat{\mu} = \bar{X} = \frac{1}{n} \sum_{i=1}^{n} X_i $$ $$ \Rightarrow \bar{X} = \frac{1}{100} \times 3,453 = 34.53 $$ ### Sample Standard Deviation Calculation The sample variance is calculated using: $$ s^2 = \frac{1}{n-1} \left\{ \sum_{i=1}^{n} X_i^2 - n \hat{\mu}^2 \right\} $$ $$ s^2 = \frac{1}{99} (800,536 - 100 \times 34.53^2) $$ $$ 34.53^2 = 1192.3209 $$ $$ 100 \times 1192.3209 = 119,232.09 $$ $$ 800,536 - 119,232.09 = 681,303.91 $$ $$ s^2 = \frac{681,303.91}{99} = 6881.857677 $$ ### Standard Deviation $$ s = \sqrt{6881.857677} = 82.96 $$ Therefore, the correct values are: - **Sample Mean = 34.53** - **Standard Deviation = 82.96**

Author: Tanishq Prabhu