Question

here are the shopping times (in minutes) for a sample of 5 shoppers at a particular computer store.

35, 42, 23, 25, 25

find the standard deviation of this sample of shopping times. round your answer to two decimal places.
(if necessary, consult a list of formulas.)

Explanation:

Calculate the sample mean

Using the Sample Mean knowledge point

$$ \bar{x} = \frac{35 + 42 + 23 + 25 + 25}{5} = \frac{150}{5} = 30 $$

Calculate the squared deviations

Using the Sample Standard Deviation knowledge point

$$
LATEXBLOCK0
$$

Sum the squared deviations

Using the Sample Standard Deviation knowledge point

$$ \sum (x_i - \bar{x})^2 = 25 + 144 + 49 + 25 + 25 = 268 $$

Calculate the sample variance

Using the Sample Standard Deviation knowledge point

$$ s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1} = \frac{268}{5 - 1} = \frac{268}{4} = 67 $$

Calculate the sample standard deviation

Using the Sample Standard Deviation knowledge point

$$ s = \sqrt{67} \approx 8.18535 $$

Answer:

8.19