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

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

Q: A student scored 34 on a test where 8 out of 25 students scored less than 34. What is the percentile rank of the score 34?

$$\frac{8}{25} \times 100 = 32$$

Question 1

Which of the following best describes the first quartile $$Q_1 in a $$data set?

Accepted Answer

It is the value below which about 25% of the data fall.

Question 2

Given the ordered data set: $$12, 15, 18, 21, 24, 27, 30, 33, 36$$, what is the median ($$Q_2$$)?

Accepted Answer

$$24$$

Question 3

A data set has $$Q_1 = 20$ and Q_3$ = 40. $$What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 40 - 20 = 20$$

Question 4

If a data set has $$Q_1 = 15$, Q_3$ = 35$$, and a value $$x = 5$$, is $$x an $$outlier?

Accepted Answer

Yes, because $$x \u003c Q_1$ - 1.5(IQR).$$

Question 5

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

Accepted Answer

The mean

Question 6

A box-and-whisker plot is constructed for a data set. The left whisker is much longer than the right. What does this suggest?

Accepted Answer

There may be an outlier on the left side of the data.

Question 7

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

Accepted Answer

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

Question 8

A student scored 34 on a test where 8 out of 25 students scored less than 34. What is the percentile rank of the score 34?

Accepted Answer

$$\frac{8}{25} 	imes 100 = 32$$

Question 9

The mean speed of cars on a highway is $$60$$ mph with a standard deviation of $$5$$ mph. What is the $$z-$$score for a car traveling at $$70$$ mph?

Accepted Answer

$$z = \frac{70 - 60}{5} = 2$$

Question 10

A woman is 72 inches tall. In her population, the mean height is $$64.3$$ inches with a standard deviation of $$2.6$$ inches. What is her $$z-$$score?

Accepted Answer

$$z = \frac{72 - 64.3}{2.6} \approx 2.96$$

Question 11

Which of the following statements about the interquartile range (IQR) is TRUE?

Accepted Answer

The IQR measures the spread of the middle 50% of the data.

Question 12

A data set has $$Q_1 = 18$, Q_3$ = 42$$, and a value $$x = 60. Is$$ $$x an $$outlier?

Accepted Answer

Yes, because $$x \u003e Q_3$ + 1.5(IQR).$$

Question 13

Which of the following best describes a standard score (z-score)?

Accepted Answer

The number of standard deviations a value is from the mean.

Question 14

If a value has a $$z-$$score of $$-2.5$$, what does this indicate about the value?

Accepted Answer

It is 2.5 standard deviations below the mean.

Question 15

Which of the following is a correct interpretation of the 80th percentile of SAT scores being 1250?

Accepted Answer

80% of students scored 1250 or less.

Question 16

A data set has the following five-number summary: Min = 10, $$Q_1 = 20$, Q_2$ = 30$$, $$Q_3 = 40$, Max = 50. What percentage of the data is expected to fall between Q_1$ and Q_3$?

Accepted Answer

About 50%

Descriptive Statistics: Measures of Position (Quartiles, Percentiles, and z-Scores)

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