Question

find the standard deviation, \\( \sigma \\), of the data. 465, 460, 497, 462, 462, 474 \\( \overline { x } = 470 \\) variance\\( ( \sigma ^ { 2 } ) = 166.3 \\) \\( \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 \(\sigma^{2} = 166.3\), then \(\sigma=\sqrt{166.3}\).

Step3: Calculate the square - root

Using a calculator, \(\sqrt{166.3}\approx12.9\) (rounded to the nearest tenth).

Answer:

\(12.9\)