find the standard deviation of the given data.\nfirst, find the mean, $\bar{x}$, of the data.\n5, 6, 8…

Explanation:

Step1: Recall mean formula

The mean $\bar{x}$ of a data - set $x_1,x_2,\cdots,x_n$ is given by $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. Here $n = 4$, $x_1=5$, $x_2 = 6$, $x_3=8$, $x_4 = 13$.

Step2: Calculate the sum of data

$\sum_{i=1}^{4}x_i=5 + 6+8 + 13=32$.

Step3: Calculate the mean

$\bar{x}=\frac{32}{4}=8$.

Answer:

$8$