Q: A data set has $$Q_1 = 15$ and Q_3$ = 35. $$What is the lower limit for identifying outliers?

$$\text{Lower limit} = Q_1$ - 1.5 \times IQR = 15 - 1.5 \times (35 - 15) = 15 - 30 = -15$$

Q: A data set has 40 values. What is the position of the 25th percentile (P$$_{25}$$)?

$$\text{Position} = \frac{25}{100} \times 40 = 10$$

Q: A student scored the 80th percentile on a standardized test in a group of 250 students. How many students scored below this student?

$$0.80 \times 250 = 200$$ students

Q: A data set has $$Q_1 = 12$, Q_3$ = 28. $$What is the semi-interquartile range?

$$\text{Semi-IQR} = \frac{Q_3$ - Q_1$}{2} = \frac{28 - 12}{2} = 8$$

Question 1

A sample of exam scores has a mean of 75 and a standard deviation of 8. What is the z-score for a student who scored 91 on the exam?

Accepted Answer

$$z = \frac{91 - 75}{8} = 2.00$$

Question 2

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

Accepted Answer

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

Question 3

Given a data set with $$Q_1 = 20$, Q_3$ = 40$$, and $$IQR = Q_3$ - Q_1$, what is the interquartile range?

Accepted Answer

$$IQR = 40 - 20 = 20$$

Question 4

A data set has $$Q_1 = 15$ and Q_3$ = 35. $$What is the lower limit for identifying outliers?

Accepted Answer

$$	ext{Lower limit} = Q_1$ - 1.5 	imes IQR = 15 - 1.5 	imes (35 - 15) = 15 - 30 = -15$$

Question 5

A hospital records the birth weights of newborns. The mean is 3200 g, and the standard deviation is 600 g. A baby weighs 4400 g. What is the z-score, and is this value significant?

Accepted Answer

$$z = \frac{4400 - 3200}{600} = 2.00$$, which is significant

Question 6

Which of the following is the correct five-number summary for the data set: 4, 8, 15, 16, 23, 42, 50?

Accepted Answer

Min = 4, $$Q_1 = 8$, Median = 16, Q_3$ = 42$$, Max = 50

Question 7

A data set has 40 values. What is the position of the 25th percentile (P$$_{25}$$)?

Accepted Answer

$$	ext{Position} = \frac{25}{100} 	imes 40 = 10$$

Question 8

A student scored the 80th percentile on a standardized test in a group of 250 students. How many students scored below this student?

Accepted Answer

$$0.80 	imes 250 = 200$$ students

Question 9

Which of the following best describes the effect of a right-skewed distribution on the location of quartiles?

Accepted Answer

$$Q_3 is $$farther from the median than $$Q_1 is$$

Question 10

A data set has $$Q_1 = 12$, Q_3$ = 28. $$What is the semi-interquartile range?

Accepted Answer

$$	ext{Semi-IQR} = \frac{Q_3$ - Q_1$}{2} = \frac{28 - 12}{2} = 8$$

Question 11

If a value in a data set has a z-score of $$-2.5$$, what can you conclude about this value?

Accepted Answer

It is significantly low compared to the mean

Question 12

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 13

A data set has the following five-number summary: Min = 10, $$Q_1 = 20$, Median = 30, Q_3$ = 40$$, Max = 100. Which value is most likely an outlier?

Accepted Answer

100

Question 14

In a class of 100 students, Jack is ranked 80th (with 1 being the top rank). Jill is at the 80th percentile. Who has the higher standing?

Accepted Answer

Jill, because 80% of students scored below her, while Jack is only above 20% of the class

Question 15

A data set has 25 values. What is the percentile of the 10th value when the data is sorted in increasing order?

Accepted Answer

$$	ext{Percentile} = \frac{10}{25} 	imes 100 = 40th $$percentile

Question 16

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

Accepted Answer

The mean

Question 17

A data set has $$Q_1 = 18$, Q_3$ = 42. $$What is the midquartile range?

Accepted Answer

$$	ext{Midquartile} = \frac{Q_1$ + Q_3$}{2} = \frac{18 + 42}{2} = 30$$

Question 18

If a data value is greater than the upper limit defined by $$Q_3 + 1.5$$ 	imes IQR$$, what does this indicate?

Accepted Answer

The value is an outlier

Question 19

A data set has the following sorted values: 5, 7, 9, 12, 15, 18, 21, 24, 27. What is the median?

Accepted Answer

15

Describing, Exploring, and Comparing Data: Measures of Relative Standing and Boxplots

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