Q: How do you calculate the percentile rank of a value $$x in a $$data set?

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

Question 1

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

Accepted Answer

The range of the middle 50% of the data, calculated as $$Q_3$$ - $$Q_1.$$

Question 2

A data set of home prices is highly skewed to the right. Which measure of center and spread should you use to best describe the data?

Accepted Answer

Median and interquartile range (IQR)

Question 3

Given the following five-number summary for tuition costs (in thousands): Min = 19, $$Q_1 = 48$, Median = 55, Q_3$ = 58$$, Max = 61. What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 58 - 48 = 10$$

Question 4

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

Accepted Answer

The student scored higher than 90% of the test-takers.

Question 5

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

Accepted Answer

Mean

Question 6

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

Accepted Answer

The value is 2.5 standard deviations below the mean.

Question 7

Suppose the mean speed on a highway is 56 mph with a standard deviation of 4 mph. What is the z-score for a car traveling at 62 mph?

Accepted Answer

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

Question 8

Which scenario best illustrates the use of z-scores for comparison?

Accepted Answer

Comparing the heights of a man and a woman relative to their respective populations.

Question 9

A box-and-whisker plot for tuition costs shows a much longer left whisker than right whisker. What does this suggest about the data?

Accepted Answer

The data are skewed to the left, possibly with outliers on the low end.

Question 10

How do you calculate the percentile rank of a value $$x in a $$data set?

Accepted Answer

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

Question 11

Which of the following statements about quartiles is TRUE?

Accepted Answer

$$Q_1 is $$the median of the lower half of the data.

Question 12

A data set has a mean of 100 and a standard deviation of 15. A value of 130 is observed. What is the z-score for this value?

Accepted Answer

$$z = \frac{130 - 100}{15} = 2.0$$

Question 13

Which of the following is a reason to use the interquartile range (IQR) instead of the range?

Accepted Answer

IQR is less affected by outliers than the range.

Question 14

If a data set is symmetrical and unimodal, which measures are most appropriate for describing the center and spread?

Accepted Answer

Mean and standard deviation

Question 15

A value is considered an outlier if it is:

Accepted Answer

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

Question 16

Which of the following best describes a fractile?

Accepted Answer

A measure that divides ordered data into equal parts based on relative position.

Descriptive Statistics: Measures of Position, Variation, and Standard Scores

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