Question

find the standard deviation, \\(\sigma\\), of the data.\
251, 224, 237, 255, 268\
\\(\overline{x} = 247\\)\
variance\\((\sigma^2) = 230\\)\
\\(\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 the formula is \(\sigma=\sqrt{\sigma^2}\).

Step2: Substitute the variance value

We know that \(\sigma^2 = 230\), so we need to calculate \(\sqrt{230}\).

Step3: Calculate the square root and round

Using a calculator, \(\sqrt{230}\approx15.2\) (rounded to the nearest tenth).

Answer:

\(15.2\)