Question 1

Given the following data set representing wait times (in minutes) for Space Mountain at 10AM: 10, 15, 15, 15, 15, 20, 20, 20, 20, 25, 25, 25, 25, 25, 30, 30, 30, 30, 30, 35, 35, 35, 35, 40, 40, 40, 45, 45, 50, 50, 50, 55, 60, 60, 65, 65, 75, 75, 105, 110. What is the value of the first quartile ($$Q_1$$)?

Accepted Answer

$$Q_1 = 25$

Question 2

Which of the following statements about z-scores is TRUE?

Accepted Answer

A z-score indicates how many standard deviations a value is from the mean.

Question 3

A temperature of 99°F is recorded among 106 adults with a sample mean $$\overline{x} = 98.20$$°F and sample standard deviation $$s = 0.62$$°F. What is the z-score for this temperature?

Accepted Answer

$$z = \frac{99 - 98.20}{0.62} = 1.29$$

Question 4

Which value is considered significantly high according to the range rule of thumb for z-scores?

Accepted Answer

A value with $$z \geq 2$$

Question 5

What is the 5-number summary for the Space Mountain wait times data set?

Accepted Answer

Minimum = 10, $$Q_1 = 25$, Median = 35, Q_3$ = 50$$, Maximum = 110

Question 6

If a value in a data set has a z-score of $$-2.5$$, what does this indicate about the value?

Accepted Answer

The value is significantly low compared to the mean.

Question 7

Which of the following best describes the third quartile ($$Q_3$$)?

Accepted Answer

$$Q_3$$ separates the bottom 75% of the data from the top 25%.

Question 8

A quarter weighs 5.7790 g. In a sample of 40 quarters with mean $$\overline{x} = 5.63930 g $$and $$s = 0.06194 g$$, what is the z-score for this quarter?

Accepted Answer

$$z = \frac{5.7790 - 5.63930}{0.06194} = 2.25$$

Question 9

Which of the following is NOT a property of percentiles?

Accepted Answer

Percentiles divide a data set into 10 equal groups.

Question 10

A boxplot is constructed for a data set. Which of the following statements is TRUE?

Accepted Answer

The box extends from $$Q_1 to$$ $$Q_3$$ and the line inside the box represents the median.

Question 11

If the 45-minute wait time for Space Mountain is at the 75th percentile, what does this mean?

Accepted Answer

75% of the wait times are less than or equal to 45 minutes.

Question 12

Which formula is used to calculate the locator $$L$$ for the $$kth $$percentile in a data set of $$n$$ values?

Accepted Answer

$$L = \frac{k}{100} 	imes n$$

Question 13

Which of the following is NOT included in the 5-number summary?

Accepted Answer

The mean

Question 14

If a value is exactly at the median of a data set, what is its percentile rank?

Accepted Answer

50th percentile

Question 15

Which of the following best describes the process for finding the value of a percentile that falls between two data points?

Accepted Answer

Average the two closest values.

Measures of Position: Z-Scores, Percentiles, Quartiles, and Boxplots

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