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

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

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 $$19 \u003c Q_1$ - 1.5(IQR) = 29.75)$$

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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