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

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

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

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

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 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?

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

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

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

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 $x < Q_1 - 1.5(IQR)$.

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 $x > Q_3 + 1.5(IQR)$.

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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