Q: Which formula is used to find the percentile of a specific data entry $x$ in a data set?

$\text{Percentile of } x = \dfrac{\text{number of entries less than } x}{\text{total number of entries}} \times 100$

Q: Given a data set with $Q_1 = 47$, $Q_3 = 58.5$, and $IQR = 11.5$, which tuition cost is considered an outlier?

$19$ (since $19 < Q_1 - 1.5(IQR) = 29.75$)

Q: A car travels at 47 mph on a highway where the mean speed is 56 mph and the standard deviation is 4 mph. What is the z-score for this car's speed?

$z = \dfrac{47 - 56}{4} = -2.25$

Q: A 6-foot-tall man (72 inches) is compared to the mean height of men ($\mu = 69.9$ in, $\sigma = 3.0$ in) and women ($\mu = 64.3$ in, $\sigma = 2.6$ in). What is the z-score for the woman?

$z = \dfrac{72 - 64.3}{2.6} \approx 2.96$

Q: Which of the following best describes the interquartile range (IQR)?

It is the difference between the third and first quartiles.

Question 1

Which of the following statements about quartiles is correct?

Accepted Answer

The third quartile $Q_3$ is the value below which about three quarters of the data fall.

Question 2

Given the data set: 19, 30, 39, 44, 45, 46, 48, 48, 48, 48, 55, 55, 55, 55, 56, 57, 57, 58, 58, 59, 59, 59, 60, 61, 61, what is the interquartile range (IQR) if $Q_1 = 47$ and $Q_3 = 58.5$?

Accepted Answer

$IQR = Q_3 - Q_1 = 58.5 - 47 = 11.5$

Question 3

A box-and-whisker plot requires which of the following components?

Accepted Answer

Minimum, $Q_1$, median ($Q_2$), $Q_3$, maximum

Question 4

If a data entry is less than $Q_1 - 1.5(IQR)$, what does this indicate?

Accepted Answer

The data entry is an outlier.

Question 5

In a box-and-whisker plot, if the left whisker is much longer than the right whisker, what does this suggest about the data?

Accepted Answer

There is a possible outlier to the left.

Question 6

Which formula is used to find the percentile of a specific data entry $x$ in a data set?

Accepted Answer

$	ext{Percentile of } x = \dfrac{	ext{number of entries less than } x}{	ext{total number of entries}} 	imes 100$

Question 7

A student scored 1350 on the SAT, which corresponds to the 90th percentile. What does this mean?

Accepted Answer

The student scored higher than 90% of the students.

Question 8

Given a data set with $Q_1 = 47$, $Q_3 = 58.5$, and $IQR = 11.5$, which tuition cost is considered an outlier?

Accepted Answer

$19$ (since $19 < Q_1 - 1.5(IQR) = 29.75$)

Question 9

Which of the following is the correct formula for the standard score (z-score)?

Accepted Answer

$z = \dfrac{x - \mu}{\sigma}$

Question 10

A car travels at 47 mph on a highway where the mean speed is 56 mph and the standard deviation is 4 mph. What is the z-score for this car's speed?

Accepted Answer

$z = \dfrac{47 - 56}{4} = -2.25$

Question 11

A 6-foot-tall man (72 inches) is compared to the mean height of men ($\mu = 69.9$ in, $\sigma = 3.0$ in) and women ($\mu = 64.3$ in, $\sigma = 2.6$ in). What is the z-score for the woman?

Accepted Answer

$z = \dfrac{72 - 64.3}{2.6} \approx 2.96$

Question 12

Which of the following best describes the interquartile range (IQR)?

Accepted Answer

It is the difference between the third and first quartiles.

Question 13

If a data set has $Q_1 = 25$, $Q_2 = 31$, and $Q_3 = 35$, what percentage of the data falls on or below $Q_2$?

Accepted Answer

About 50%

Question 14

Which of the following is NOT a fractile?

Accepted Answer

Mode

Question 15

A data set has $Q_1 = 26$, $Q_2 = 31$, $Q_3 = 35$. What is the IQR and what range of values would be considered outliers?

Accepted Answer

$IQR = 35 - 26 = 9$. Outliers are less than $26 - 1.5 	imes 9 = 12.5$ or greater than $35 + 1.5 	imes 9 = 48.5$.

Question 16

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

Accepted Answer

A z-score of 0 means the value is equal to the mean.

Question 17

If a student’s test score is at the 60th percentile, what does this indicate?

Accepted Answer

The student scored higher than 60% of the students.

Question 18

Which of the following is NOT part of the five-number summary used in a box-and-whisker plot?

Accepted Answer

Mean

Measures of Position in Descriptive Statistics

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