Question

the ages (in years) of a random sample of shoppers at a gaming store are shown. determine the range, mean, variance, and standard deviation of the sample data set. 12, 15, 23, 14, 14, 17, 21, 18, 13, 17. the range is 11. (simplify your answer.) the mean is 16.4. (simplify your answer. round to the nearest tenth as needed.) the variance is 12.5. (simplify your answer. round to the nearest tenth as needed.) the standard deviation is. (simplify your answer. round to the nearest tenth as needed.)

Explanation:

Step1: Recall the formula for standard deviation

The standard deviation $\sigma$ of a sample is the square root of the variance $s^{2}$. So, $\sigma=\sqrt{s^{2}}$.

Step2: Substitute the value of variance

Given that the variance $s^{2} = 12.5$. Then $\sigma=\sqrt{12.5}$.

Step3: Calculate the square - root

Using a calculator, $\sqrt{12.5}\approx3.5$.

Answer:

$3.5$