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, 21, 23, 14, 16, 18, 19, 17, 13, 16

the range is 11.
(simplify your answer.)

the mean is 16.9.
(simplify your answer. round to the nearest tenth as needed.)

the variance is 12.1.
(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:

Identify the given values and target unknown

The problem provides a sample dataset of ages:

$$ 12, 21, 23, 14, 16, 18, 19, 17, 13, 16 $$

The range, mean, and sample variance have already been calculated and filled in:

• Range: \(11\)
• Mean: \(16.9\)
• Variance: \(12.1\)

We need to find the sample standard deviation, rounded to the nearest tenth.

Calculate the sample standard deviation

Using the Sample Standard Deviation knowledge point

$$ s = \sqrt{s^2} = \sqrt{12.1} \approx 3.4785 $$

Round to the nearest tenth

Rounding \(3.4785\) to the nearest tenth yields:

$$ s \approx 3.5 $$

Answer:

The standard deviation is <blank>\(3.5\)</blank>