Question

find the standard deviation, (sigma), of the data. 16, 13, 20, 16, 12, 17, 18 (overline{x}=16) variance((sigma^{2}) = 6.6) (sigma = ?) round to the nearest tenth

Explanation:

Step1: Recall the relationship between variance and standard deviation

The standard deviation \(\sigma\) is the square root of the variance \(\sigma^{2}\). So the formula is \(\sigma=\sqrt{\sigma^{2}}\).

Step2: Substitute the value of variance

Given \(\sigma^{2} = 6.6\), then \(\sigma=\sqrt{6.6}\).
Using a calculator, \(\sqrt{6.6}\approx2.569\).

Step3: Round to the nearest tenth

Rounding \(2.569\) to the nearest tenth, we look at the hundredth - digit. The hundredth - digit is \(6\), so we round up the tenth - digit. So \(2.569\approx2.6\).

Answer:

\(2.6\)