Question

find the standard deviation, (sigma), of the data. 56, 52, 46, 49, 57, 64 (overline{x}=54) variance((sigma^{2}) = 34.3) (sigma=) ? round to the nearest tenth

Explanation:

Step1: Recall the relationship between standard deviation and variance

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 $\sigma^{2} = 34.3$, then $\sigma=\sqrt{34.3}$.
Using a calculator, $\sqrt{34.3}\approx5.8566$.

Step3: Round to the nearest tenth

Rounding 5.8566 to the nearest tenth. The digit in the hundredth place is 5, so we round up the digit in the tenth place. So, 5.8566 $\approx5.9$.

Answer:

$5.9$