$$ \left. \begin{array} { l }{ s = \sqrt { \frac { 1 } { n - 1 } ( \sum x ^ { 2 } - n \overline { x } ^ { 2 } ) } } \ { = \sqrt { \frac { 1 } { 8 - 1 } ( 42206,85 - 8 ( 72,2375 ) ^ { 2 } ) } } \ { = \sqrt { 65,828 \ldots } } \ { \approx 8,11 m } \end{array} ight. $$

Question

$$ \left. \begin{array} { l }{ s = \sqrt { \frac { 1 } { n - 1 } ( \sum x ^ { 2 } - n \overline { x } ^ { 2 } ) } } \ { = \sqrt { \frac { 1 } { 8 - 1 } ( 42206,85 - 8 ( 72,2375 ) ^ { 2 } ) } } \ { = \sqrt { 65,828 \ldots } } \ { \approx 8,11 m } \end{array} ight. $$

UpStudy AI · Accepted Answer

1. We start with the formula for the sample standard deviation:
   $$
   s = \sqrt{\frac{1}{n-1}\left(\sum x^2 - n\overline{x}^2\right)}
   $$

2. Given $$ n = 8 $$, the formula becomes:
   $$
   s = \sqrt{\frac{1}{8-1}\left(\sum x^2 - 8\overline{x}^2\right)}
   $$

3. Substitute the provided values:
   $$
   \sum x^2 = 42206,85 \quad \text{and} \quad \overline{x} = 72,2375
   $$
   Thus,
   $$
   s = \sqrt{\frac{1}{7}\left(42206,85 - 8 \left(72,2375\right)^2\right)}
   $$

4. Compute the expression inside the parentheses:
   $$
   8\overline{x}^2 = 8 \left(72,2375\right)^2
   $$
   and then subtract from $$\sum x^2$$:
   $$
   \sum x^2 - 8\overline{x}^2
   $$
   (This difference is given as approximately $$42206,85 - 8 \left(72,2375\right)^2$$.)

5. Divide the result by $$7$$:
   $$
   \frac{1}{7}\left(42206,85 - 8\left(72,2375\right)^2\right) \approx 65,828\ldots
   $$

6. Finally, take the square root:
   $$
   s = \sqrt{65,828\ldots} \approx 8,11\, m
   $$

Thus, the computed sample standard deviation is approximately $$8,11\, m$$.
The sample standard deviation is approximately $$8.11\, m$$.

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