Question

find the standard deviation, \\( \sigma \\), of the data. 78, 45, 73, 66, 61, 67 \\( \overline { x } = 65 \\) variance\\( ( \sigma ^ { 2 } ) = 109 \\) \\( \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 $\sigma^{2} = 109$, then $\sigma=\sqrt{109}$.

Step3: Calculate the square - root

Using a calculator, $\sqrt{109}\approx10.4403$.

Step4: Round to the nearest tenth

Rounding $10.4403$ to the nearest tenth gives $10.4$.

Answer:

$10.4$