Question

find the mean, variance, and standard deviation for the data set. 7, 15, 9, 5, 11, 8, 13, 4, 19, 9 the mean is \\( \bar{x} = 10.00 \\) (round to two decimal places as needed). the variance is \\( \sigma^2 = 19.20 \\) (round to two decimal places as needed). the standard deviation is \\( \sigma \approx \square \\) (round to two decimal places as needed).

Explanation:

Step1: Recall the formula for standard deviation

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

Step2: Substitute the variance value

We know that the variance \(\sigma^2 = 19.20\). So we need to calculate \(\sqrt{19.20}\).
Using a calculator, \(\sqrt{19.20}\approx4.38\) (rounded to two decimal places).

Answer:

\(4.38\)