Question

find the standard deviation, \\( \sigma \\), of the data.
95, 80, 191, 86, 122, 86
\\( \overline { x } = 110 \\)
\\( \operatorname { variance } ( \sigma ^ { 2 } ) = 1,497 \\)
\\( \sigma = ? \\)
round to the nearest tenth.

Explanation:

Step1: Recall the formula for standard deviation

The formula for standard deviation \(\sigma\) is \(\sigma=\sqrt{\text{Variance}}\).

Step2: Substitute the given variance value

Given \(\text{Variance}(\sigma^{2}) = 1497\), so \(\sigma=\sqrt{1497}\).

Step3: Calculate the square - root

Using a calculator, \(\sqrt{1497}\approx38.7\)

Answer:

\(38.7\)