Question

find the standard deviation, $\sigma$, of the data. 147, 141, 120, 124, 128 $\overline{x} = 132$ variance($\sigma^2$) = 106 $\sigma = ?$ 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 variance value

Given that the variance \(\sigma^2 = 106\), we calculate \(\sigma=\sqrt{106}\).

Step3: Calculate the square root and round

\(\sqrt{106}\approx10.3\) (rounded to the nearest tenth).

Answer:

\(10.3\)