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 given variance value

Given \(\sigma^{2} = 230\), then \(\sigma=\sqrt{230}\).

Step3: Calculate the square - root

Using a calculator, \(\sqrt{230}\approx15.2\) (rounded to the nearest tenth).

Answer:

\(15.2\)