Q: A data set of 50 marathon finish times is sorted in increasing order. What is the locator $L$ for the 40th percentile?

$L = \frac{40}{100} \times 50 = 20$

Q: A data value is considered an outlier in a modified boxplot if it is:

More than $1.5 \times IQR$ above $Q_3$ or below $Q_1$

Q: A data set has $Q_1 = 20$, $Q_3 = 40$, and $IQR = 20$. What is the upper boundary for non-outlier values in a modified boxplot?

$Q_3 + 1.5 \times IQR = 40 + 1.5 \times 20 = 70$

Question 1

A hospital is comparing the cholesterol levels of two patients. Patient A has a cholesterol level of 220 mg/dL (sample mean = 200 mg/dL, sample standard deviation $s = 10$ mg/dL). Patient B has a cholesterol level of 180 mg/dL (sample mean = 170 mg/dL, sample standard deviation $s = 5$ mg/dL). Which patient’s cholesterol level is more extreme relative to their respective group?

Accepted Answer

Patient A, because their z score is higher.

Question 2

Which formula would you use to calculate the z score for a value $x$ from a sample with mean $\overline{x}$ and standard deviation $s$?

Accepted Answer

$z = \frac{x - \overline{x}}{s}$

Question 3

A student’s exam score has a z score of $-2.5$. What does this indicate about the student’s performance?

Accepted Answer

The student’s score is significantly low.

Question 4

Given a data set with mean $\mu = 50$ and standard deviation $\sigma = 8$, what is the z score for a value $x = 66$?

Accepted Answer

$z = \frac{66 - 50}{8} = 2$

Question 5

A value is considered significantly high if its z score is:

Accepted Answer

Greater than or equal to $+2$

Question 6

A data set of 50 marathon finish times is sorted in increasing order. What is the locator $L$ for the 40th percentile?

Accepted Answer

$L = \frac{40}{100} 	imes 50 = 20$

Question 7

If a value is at the 72nd percentile in a data set, what does this mean?

Accepted Answer

72% of the data values are less than this value.

Question 8

Which of the following is NOT part of the 5-number summary?

Accepted Answer

The mean

Question 9

Given the following 5-number summary for a data set: 12, 18, 25, 32, 45. What is the interquartile range (IQR)?

Accepted Answer

$IQR = Q_3 - Q_1 = 32 - 18 = 14$

Question 10

A boxplot is constructed for a data set. If the median is closer to $Q_1$ than $Q_3$, and the right whisker is longer than the left, what can you infer about the distribution?

Accepted Answer

The distribution is skewed right.

Question 11

Which of the following statements about z scores is FALSE?

Accepted Answer

A z score is always positive.

Question 12

A data value is considered an outlier in a modified boxplot if it is:

Accepted Answer

More than $1.5 	imes IQR$ above $Q_3$ or below $Q_1$

Question 13

Which of the following best describes the midquartile of a data set?

Accepted Answer

$\frac{Q_1 + Q_3}{2}$

Question 14

If the 10th percentile of a data set is 15 and the 90th percentile is 85, what is the 10–90 percentile range?

Accepted Answer

$P_{90} - P_{10} = 85 - 15 = 70$

Question 15

A data set has $Q_1 = 20$, $Q_3 = 40$, and $IQR = 20$. What is the upper boundary for non-outlier values in a modified boxplot?

Accepted Answer

$Q_3 + 1.5 	imes IQR = 40 + 1.5 	imes 20 = 70$

Question 16

Which of the following is true about quartiles?

Accepted Answer

$Q_2$ is the same as the median.

Question 17

A data set has a minimum of 5, $Q_1 = 10$, median = 15, $Q_3 = 20$, and maximum of 30. Which value would be represented by the right edge of the box in a boxplot?

Accepted Answer

$Q_3 = 20$

Question 18

If a value is at the 25th percentile, which quartile does it correspond to?

Accepted Answer

$Q_1$

Question 19

A researcher finds that a data value has a z score of 0. What does this indicate?

Accepted Answer

The value is equal to the mean.

Measures of Relative Standing and Boxplots: Chapter 3 Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards