Q: Given a data set with $$Q_1 = 20$, Q_3$ = 40$$, and $$IQR = 20$$, which value would be considered an outlier?

A value greater than $$Q_3 + 1.5$$ \times IQR = 40 + 1.5 \times 20 = 70$$

Q: In a class of 40 students, you have the 5th highest score. What is your percentile rank?

$$\frac{35}{40} \times 100 = 87.5$$ percentile

Q: A data set has $$Q_1 = 15$, Q_3$ = 25$$, and a value of 5. Is 5 an outlier?

No, because $$5 \u003e Q_1$ - 1.5 \times (Q_3$ - Q_1$) = 15 - 1.5 \times 10 = 0$$

Q: Which of the following is the correct formula for finding the percentile rank of a value $$x in a $$data set of size $$n$$?

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

Question 1

A student scored 85 on a statistics exam where the class mean was 75 and the standard deviation was 5. What is the student's z-score?

Accepted Answer

$$z = \frac{85 - 75}{5} = 2$$

Question 2

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 3

Given a data set with $$Q_1 = 20$, Q_3$ = 40$$, and $$IQR = 20$$, which value would be considered an outlier?

Accepted Answer

A value greater than $$Q_3 + 1.5$$ 	imes IQR = 40 + 1.5 	imes 20 = 70$$

Question 4

In a class of 40 students, you have the 5th highest score. What is your percentile rank?

Accepted Answer

$$\frac{35}{40} 	imes 100 = 87.5$$ percentile

Question 5

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

Accepted Answer

Mean

Question 6

A boxplot shows a long whisker on the right side. What does this indicate about the data distribution?

Accepted Answer

The data is skewed to the right (positively skewed).

Question 7

If a value has a z-score of -2.5, how would you describe this value?

Accepted Answer

It is significantly low.

Question 8

Given the following 5-number summary: Min = 10, $$Q_1 = 20$, Median = 30, Q_3$ = 40$$, Max = 100. Which value is most likely an outlier?

Accepted Answer

100

Question 9

Which formula is used to calculate the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$

Question 10

A student scored 1200 on the SAT (mean = 1080, SD = 170) and 28 on the ACT (mean = 22, SD = 5). Which test did the student perform better on, relative to their peers?

Accepted Answer

ACT, because $$z = \frac{28-22}{5} = 1.2$$ and SAT $$z = \frac{1200-1080}{170} \approx 0.71$$

Question 11

If the 40th percentile of a data set corresponds to the 8th value in an ordered list of 20 values, how do you find the value at the 40th percentile?

Accepted Answer

Take the average of the 8th and 9th values.

Question 12

Which of the following best describes the effect of an outlier on the mean and standard deviation?

Accepted Answer

Both the mean and standard deviation can be dramatically affected by outliers.

Question 13

A data set has $$Q_1 = 15$, Q_3$ = 25$$, and a value of 5. Is 5 an outlier?

Accepted Answer

No, because $$5 \u003e Q_1$ - 1.5 	imes (Q_3$ - Q_1$) = 15 - 1.5 	imes 10 = 0$$

Question 14

Which of the following is the correct formula for finding the percentile rank of a value $$x in a $$data set of size $$n$$?

Accepted Answer

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

Question 15

Which of the following is NOT a property of z-scores?

Accepted Answer

A z-score can never be negative.

Question 16

A boxplot is constructed for a data set. Which feature would indicate the presence of outliers?

Accepted Answer

Dots or asterisks plotted beyond the whiskers.

Question 17

If the minimum value in a data set is 10, $$Q_1 = 20$, median = 30, Q_3$ = 40$$, and the maximum is 100, what is the interquartile range?

Accepted Answer

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

Question 18

Which of the following best describes the 5-number summary?

Accepted Answer

Minimum, $$Q_1$$, Median, $$Q_3$$, Maximum

Measures of Relative Standing and Boxplots: Study Notes for Introductory Statistics

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