Question

now use the defining formula for sample standard deviation $s = sqrt{\frac{sum(x - \bar{x})^2}{n - 1}}$ with $n = 5$. recall that the sum is taken over all data values. simplify and round the final answer to two decimal places.
$s=sqrt{\frac{sum(x - \bar{x})^2}{n - 1}}
=sqrt{\frac{11.56 + 1.96+0.36+square+6.76}{5 - 1}}
=sqrt{\frac{square}{4}}
=square$

Explanation:

Step1: Calculate the sum in the numerator

First, add the given numbers: $11.56+1.96 + 0.36+6.76=20.64$.

Step2: Divide by $n - 1$

Since $n = 5$, $n-1=4$. So, $\frac{20.64}{4}=5.16$.

Step3: Take the square - root

$s=\sqrt{5.16}\approx2.27$.

Answer:

$2.27$