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

$$Therefore, the correct values are: - **Sample Mean = 34.53** - **Standard Deviation = 82.96**$$