rylan is calculating the standard deviation of a data set that has 9 values. he determines that the sum of…

Explanation:

Step1: Recall standard - deviation formula

The formula for the sample standard deviation $s$ is $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$, where $\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}$ is the sum of squared deviations and $n$ is the number of data - points. Here, $\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}=316$ and $n = 9$.

Step2: Calculate the denominator

The denominator $n - 1=9 - 1=8$.

Step3: Calculate the value inside the square - root

$\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}=\frac{316}{8}=39.5$.

Step4: Calculate the standard deviation

$s=\sqrt{39.5}\approx6.3$.

Answer:

$6.3$