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

Explanation:

Identify the sample data set

We are given the following sample of shopper ages:

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

The sample size is \(n = 10\).

Calculate the sample mean

Using the Mean Calculation knowledge point

$$ \bar{x} = \frac{\sum x_i}{n} = \frac{12 + 21 + 23 + 14 + 16 + 18 + 19 + 17 + 13 + 16}{10} = \frac{169}{10} = 16.9 $$

Calculate the sample variance

Using the Sample Standard Deviation knowledge point

$$
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$$

Calculate the sample standard deviation

Using the Sample Standard Deviation knowledge point

$$ s = \sqrt{s^2} = \sqrt{12.1} \approx 3.4785 \approx 3.5 $$

Answer:

The mean is <blank>\(16.9\)</blank>