Question

recall the defining formula used to compute the sample standard deviation $s = \sqrt{\frac{\sum(x - \bar{x})^2}{n - 1}}$ where $x$ is a member of the data set, $\bar{x}$ is the mean, and $n$ is the number of data values. before using the formula, we must determine $\bar{x}$ and $n$. there are five values in the data set 1, 3, 5, 6, 7, so $n = \square$. calculate the mean $\bar{x}=\frac{\sum x}{n}$ by taking the average of the data values, which is dividing the sum of the data values by the number of data values. $\bar{x}=\frac{\sum x}{n}=\frac{1 + 3+5 + 6+7}{\square}=\frac{\square}{5}=\square$

Explanation:

Step1: Determine number of data - points

The data set is 1, 3, 5, 6, 7. The number of data - points $n$ is the count of values in the set. So $n = 5$.

Step2: Calculate the sum of data - values

$\sum x=1 + 3+5 + 6+7=22$.

Step3: Calculate the mean

The mean $\bar{x}=\frac{\sum x}{n}$. Substituting $\sum x = 22$ and $n = 5$, we get $\bar{x}=\frac{22}{5}=4.4$.

Answer:

$n = 5$, $\bar{x}=4.4$