Question

find the standard deviation, \\(sigma\\), of
the data.
84, 98, 70, 76, 88, 76
\\(\bar{x} = 82\\)
variance(\\(sigma^2\\)) = 85.3
\\(sigma = ?\\)
(rounded 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 the formula is \(\sigma=\sqrt{\sigma^2}\).

Step2: Substitute the variance value

We know that \(\sigma^2 = 85.3\), so we calculate \(\sigma=\sqrt{85.3}\).

Step3: Calculate the square root

Using a calculator, \(\sqrt{85.3}\approx9.2\) (rounded to the nearest tenth).

Answer:

\(9.2\)