Question 1

A hospital administrator wants to summarize the average length of stay (in days) for all patients discharged in the past month. Which formula should be used to calculate the population mean, $$\mu$$, if the data for all patients is available?

Accepted Answer

$$\mu = \frac{\sum x_i}{N}$$

Question 2

A sample of 8 students recorded the following commute times (in minutes): 10, 12, 15, 18, 20, 22, 25, 30. What is the median commute time?

Accepted Answer

$$M = \frac{18 + 20}{2} = 19$$

Question 3

Which of the following best describes a resistant statistic?

Accepted Answer

A statistic that is not substantially affected by extreme values in the data set.

Question 4

A real estate agent finds the mean asking price for homes in a city is $$168,320, while the median is 148$$,700. What can you infer about the shape of the distribution?

Accepted Answer

The distribution is skewed right.

Question 5

Given the following data set: 4, 7, 7, 9, 10, 12, 12, 12, 15, what is the mode?

Accepted Answer

12

Question 6

A company wants to compare the variability in wait times at two restaurants. If the standard deviation at Restaurant A is 0.74 minutes and at Restaurant B is 1.27 minutes, what does this indicate?

Accepted Answer

Wait times at Restaurant B are more dispersed than at Restaurant A.

Question 7

Which formula should be used to calculate the sample standard deviation, $$s$$, for a data set?

Accepted Answer

$$s = \sqrt{\frac{\sum (x_i - \bar{x})^2$}{n-1}}$$

Question 8

A student scored 85 on a test where the mean was 75 and the standard deviation was 5. What is the student’s z-score?

Accepted Answer

$$z = \frac{85 - 75}{5} = 2$$

Question 9

Which of the following statements about the Empirical Rule is correct for a bell-shaped distribution?

Accepted Answer

Approximately 68% of the data lie within 1 standard deviation of the mean.

Question 10

A data set has $$Q_1 = 28$, Q_3$ = 38. $$What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 38 - 28 = 10$$

Question 11

A student’s SAT score is at the 90th percentile. What does this mean?

Accepted Answer

The student scored as high or higher than 90% of the test-takers.

Question 12

Given a data set with $$Q_1 = 12$, Q_3$ = 14.4$$, and $$IQR = 2.4$$, what is the lower fence for detecting outliers?

Accepted Answer

$$Lower\ Fence = Q_1$ - 1.5(IQR) = 12 - 1.5(2.4) = 8.4$$

Question 13

A boxplot of exam scores shows a long whisker on the right and the median closer to the left of the box. What does this indicate about the distribution of scores?

Accepted Answer

The distribution is skewed right.

Question 14

If a data set has a mean of 50 and a standard deviation of 8, what percentage of data falls between 34 and 66 according to the Empirical Rule?

Accepted Answer

Approximately 95%

Question 15

Which formula is used to approximate the mean from grouped data in a frequency distribution?

Accepted Answer

$$\bar{x} = \frac{\sum x_i f_i}{\sum f_i}$$

Question 16

A nutritionist combines 2 lbs of almonds at $$4/lb and 3 lbs of walnuts at 6/lb. $$What is the weighted mean price per pound?

Accepted Answer

$$\bar{x}_w = \frac{2 	imes 4 + 3 	imes 6}{2 + 3} = \frac{8 + 18}{5} = 5.2$$

Question 17

Which of the following is NOT part of the five-number summary?

Accepted Answer

The mean

Numerically Summarizing Data: Measures of Central Tendency, Dispersion, and Position

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