Q: Given a data set with $Q_1 = 20$, $Q_3 = 40$, and a value of 50, is 50 considered an outlier according to the modified boxplot rule?

No, because $50 < Q_3 + 1.5 \times IQR$

Q: A data set has 40 values. What is the percentile rank of a value that has 30 values less than it?

$P = \frac{30}{40} \times 100 = 75$th percentile

Q: Which value is the median in the following sorted data set: [5, 7, 9, 12, 15, 18, 20, 22]?

The average of 12 and 15, so $\frac{12 + 15}{2} = 13.5$

Q: If $Q_1 = 25$, $Q_3 = 45$, and the minimum and maximum values are 10 and 60, what is the interquartile range (IQR)?

$IQR = Q_3 - Q_1 = 45 - 25 = 20$

Q: A boxplot shows the median closer to $Q_1$ than $Q_3$ and the right whisker is longer than the left. What does this indicate about the distribution?

The distribution is skewed right (positively skewed).

Q: A football coach’s salary is an outlier in a data set if it is above $Q_3$ by more than $1.5 \times IQR$. If $Q_3 = 500$, $IQR = 100$, and the coach earns $700$, is this salary an outlier?

Yes, because $700 > 500 + 1.5 \times 100 = 650$

Question 1

A student scored 82 on a test with a mean of 75 and a standard deviation of 4. What is the z-score for this student’s test result?

Accepted Answer

$z = \frac{82 - 75}{4} = 1.75$

Question 2

Which of the following statements about z-scores is TRUE?

Accepted Answer

A z-score indicates how many standard deviations a value is from the mean.

Question 3

Given a data set with $Q_1 = 20$, $Q_3 = 40$, and a value of 50, is 50 considered an outlier according to the modified boxplot rule?

Accepted Answer

No, because $50 < Q_3 + 1.5 	imes IQR$

Question 4

If a value has a z-score of $-2.5$, how would you categorize it?

Accepted Answer

Significantly low

Question 5

A data set has 40 values. What is the percentile rank of a value that has 30 values less than it?

Accepted Answer

$P = \frac{30}{40} 	imes 100 = 75$th percentile

Question 6

Which value is the median in the following sorted data set: [5, 7, 9, 12, 15, 18, 20, 22]?

Accepted Answer

The average of 12 and 15, so $\frac{12 + 15}{2} = 13.5$

Question 7

Which of the following is NOT part of the 5-number summary?

Accepted Answer

Mean

Question 8

If $Q_1 = 25$, $Q_3 = 45$, and the minimum and maximum values are 10 and 60, what is the interquartile range (IQR)?

Accepted Answer

$IQR = Q_3 - Q_1 = 45 - 25 = 20$

Question 9

A boxplot shows the median closer to $Q_1$ than $Q_3$ and the right whisker is longer than the left. What does this indicate about the distribution?

Accepted Answer

The distribution is skewed right (positively skewed).

Question 10

Which formula is used to find the position (index) of the $k$th percentile in a data set of $n$ values?

Accepted Answer

$I = \frac{k}{100} 	imes n$

Question 11

A football coach’s salary is an outlier in a data set if it is above $Q_3$ by more than $1.5 	imes IQR$. If $Q_3 = 500$, $IQR = 100$, and the coach earns $700$, is this salary an outlier?

Accepted Answer

Yes, because $700 > 500 + 1.5 	imes 100 = 650$

Question 12

Which of the following best describes the purpose of a boxplot?

Accepted Answer

To visually display the distribution, center, and spread of a data set, including possible outliers.

Question 13

A student’s IQ is 80. If the mean IQ is 100 and the standard deviation is 15, what is the z-score and is it significantly low?

Accepted Answer

$z = \frac{80 - 100}{15} = -1.33$, not significantly low

Question 14

Which of the following is TRUE about outliers in a data set?

Accepted Answer

Outliers can dramatically affect the mean and standard deviation.

Question 15

If a data value is less than the mean, what can you say about its z-score?

Accepted Answer

The z-score is negative.

Question 16

Which of the following is the correct formula for a z-score for sample data?

Accepted Answer

$z = \frac{x - \overline{x}}{s}$

Question 17

A boxplot for a data set shows a long left whisker and the median closer to $Q_3$. What does this suggest about the data?

Accepted Answer

The data is skewed left (negatively skewed).

Question 18

If the 5-number summary of a data set is: 10, 20, 30, 40, 50, what is the range of the data?

Accepted Answer

$50 - 10 = 40$

Question 19

Which of the following is TRUE about quartiles?

Accepted Answer

$Q_2$ is the same as the median.

Descriptive Statistics: Measures of Relative Standing (z-scores, Quartiles, Percentiles, Box Plots)

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