Question

find the standard deviation, (sigma), of the data. 16, 13, 20, 16, 12, 17, 18 (\bar{x}=16) variance((sigma^{2}) = 6.6) (sigma=) ?

Explanation:

Step1: Recall the formula for standard deviation

The standard deviation $\sigma$ is the square root of the variance $\sigma^{2}$. So, $\sigma=\sqrt{\sigma^{2}}$.

Step2: Substitute the value of variance

Given $\sigma^{2} = 6.6$, then $\sigma=\sqrt{6.6}$.
Using a calculator, $\sqrt{6.6}\approx2.569$.

Step3: Round to the nearest tenth

Rounding $2.569$ to the nearest tenth. The digit in the hundredth place is $6$, so we round up the digit in the tenth place. So, $2.569\approx2.6$.

Answer:

$2.6$