Question

find the standard deviation, \\( \sigma \\), of the data. 251, 224, 237, 255, 268 \\( \overline { x } = 247 \\) variance\\( ( \sigma ^ { 2 } ) = 230 \\) \\( \sigma = \\) ? round to the nearest tenth

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 $\sigma^{2} = 230$. Then $\sigma=\sqrt{230}$.

Step3: Calculate the square - root

Using a calculator, $\sqrt{230}\approx15.2$.

Answer:

$15.2$