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

$$\text{Percentile of } x = \frac{\text{number of values less than } x}{n} \times 100$$

Q: A data set has $$Q_1 = 54$, Q_3$ = 68.5$$, and $$IQR = 14.5. $$What is the lower boundary for outliers?

$$Q_1 - 1.5$$ \times IQR = 54 - 1.5 \times 14.5 = 32.75$$

Question 1

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

Accepted Answer

The difference between the third quartile ($$Q_3) $$and the first quartile ($$Q_1$$): $$IQR = Q_3$ - Q_1$

Question 2

A data set of 25 tuition costs (in thousands of dollars) for liberal arts colleges is given. If $$Q_1 = 55$, Q_2$ = 64$$, and $$Q_3 = 68.5$, what is the interquartile range (IQR)?

Accepted Answer

$$IQR = 68.5 - 55 = 13.5$$

Question 3

Which of the following statements about quartiles is TRUE?

Accepted Answer

The third quartile ($$Q_3) is $$the median of the data entries to the right of the median.

Question 4

Given the following ordered data set: 23, 23, 28, 28, 28, 29, 30, 31, 31, 35, 35, 36, 37, 37. What is the median ($$Q_2$$)?

Accepted Answer

30

Question 5

A box-and-whisker plot requires which of the following five-number summary values?

Accepted Answer

Minimum, first quartile, median, third quartile, maximum

Question 6

If a data entry is less than $$Q_1 - 1.5$$ 	imes IQR$$, what can you conclude about this data entry?

Accepted Answer

It is an outlier.

Question 7

A student scored 1150 on the SAT, which is at the 70th percentile. What does this mean?

Accepted Answer

The student scored higher than 70% of the other students.

Question 8

Given a data set with mean $$\mu = 56$$ and standard deviation $$\sigma = 4$$, what is the z-score for a value $$x = 62$$?

Accepted Answer

$$z = \frac{62 - 56}{4} = 1.5$$

Question 9

Which of the following z-scores would be considered 'very unusual' according to the Empirical Rule?

Accepted Answer

$$z = 3.2$$

Question 10

A 6-foot-tall woman has a mean height of $$64.3$$ inches and a standard deviation of $$1.8$$ inches in her population. What is her z-score? (Note: 6 feet = 72 inches)

Accepted Answer

$$z = \frac{72 - 64.3}{1.8} \approx 4.28$$

Question 11

If a data set is highly skewed to the left, which of the following is most likely TRUE about the box-and-whisker plot?

Accepted Answer

The left whisker will be longer than the right whisker.

Question 12

Which formula is used to find the percentile rank of a specific data entry $$x in an $$ordered data set of $$n$$ entries?

Accepted Answer

$$	ext{Percentile of } x = \frac{	ext{number of values less than } x}{n} 	imes 100$$

Question 13

A data set has $$Q_1 = 54$, Q_3$ = 68.5$$, and $$IQR = 14.5. $$What is the lower boundary for outliers?

Accepted Answer

$$Q_1 - 1.5$$ 	imes IQR = 54 - 1.5 	imes 14.5 = 32.75$$

Question 14

Which of the following best describes a z-score of zero?

Accepted Answer

The data value is equal to the mean.

Question 15

A data set has a mean of 50 and a standard deviation of 5. If a value is 40, what is its z-score?

Accepted Answer

$$z = \frac{40 - 50}{5} = -2$$

Descriptive Statistics: Measures of Position and Variation

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