Question 1

Which of the following best describes the five-number summary displayed in a boxplot?

Accepted Answer

Minimum, first quartile ($$Q_1$$), median, third quartile ($$Q_3$$), maximum

Question 2

Given the SAT scores: 1180, 1190, 1200, 1210, 1220, 1230, 1240, 1250, 1260, 1270, 1280, 1290, 1300, 1310, 1320, what is the median?

Accepted Answer

$$1250$$

Question 3

If a boxplot for a dataset shows that $$Q_1 = 1200$, Q_3$ = 1300$$, and the median is $$1250$$, what is the interquartile range (IQR)?

Accepted Answer

$$100$$

Question 4

A boxplot of SAT scores for juniors and seniors shows that the median for juniors is $$1250$$ and for seniors is $$1300. $$Which group has the higher median SAT score?

Accepted Answer

Seniors

Question 5

In a boxplot, what does the length of the box represent?

Accepted Answer

The interquartile range ($$Q_3$$ - $$Q_1)$$

Question 6

Given the following data set of number of songs in playlists: 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, what is the value of $$Q_1$$?

Accepted Answer

$$13$$

Question 7

If a boxplot shows a much longer whisker on the right side than on the left, what does this indicate about the distribution?

Accepted Answer

The data is skewed to the right (positively skewed)

Question 8

A boxplot for two classes shows that Class A has a range of $$200$$ and Class B has a range of $$150. $$What does this tell you about the variability of scores?

Accepted Answer

Class A has greater variability in scores

Question 9

If the minimum SAT score in a boxplot is $$1180$$ and the maximum is $$1350$$, what is the range?

Accepted Answer

$$170$$

Question 10

Which of the following statements is TRUE about outliers in a boxplot?

Accepted Answer

Outliers are typically plotted as individual points beyond the whiskers

Question 11

A researcher compares the SAT scores of two groups using boxplots. Group 1 has a median of $$1200$$ and Group 2 has a median of $$1300. $$The IQR for Group 1 is $$100$$ and for Group 2 is $$50. $$What can be concluded?

Accepted Answer

Group 2 has a higher median but less variability in scores

Question 12

If the first quartile ($$Q_1) of a $$data set is $$1200$$ and the third quartile ($$Q_3) is$$ $$1300$$, what is the formula for the interquartile range?

Accepted Answer

$$IQR = Q_3$ - Q_1$

Question 13

A boxplot for SAT scores shows the following five-number summary: Min = $$1180$$, $$Q_1 = 1200$, Median = 1250$, Q_3$ = 1300$$, Max = $$1350. $$What percentage of the data falls between $$Q_1$$ and $$Q_3$$?

Accepted Answer

$$50\%$$

Question 14

If a boxplot for a data set is very short (the box and whiskers are close together), what does this indicate about the data?

Accepted Answer

The data has low variability

Question 15

Given the data set: 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, what is the maximum value?

Accepted Answer

$$24$$

Question 16

A boxplot is constructed for the number of songs in playlists: 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24. What is the range of the data?

Accepted Answer

$$15$$

Question 17

If the median of a data set is closer to $$Q_1$$ than to $$Q_3 in a $$boxplot, what does this suggest about the distribution?

Accepted Answer

The data is skewed to the right

Question 18

Which of the following is NOT a component of the five-number summary used in boxplots?

Accepted Answer

Mean

Question 19

A boxplot for SAT scores shows the minimum at $$1180$$, $$Q_1 at$$ $$1200$$, median at $$1250$$, $$Q_3 at$$ $$1300$$, and maximum at $$1350. $$What is the value of the third quartile?

Accepted Answer

$$1300$$

Question 20

If a boxplot for two groups shows that Group A has a higher maximum but a lower median than Group B, what can be inferred?

Accepted Answer

Group A has a wider spread but lower central tendency

Boxplots: Displaying and Interpreting the Five Number Summary

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