Exercises for Question Type 7: Comparing two different data sets of box and whiskers

Question 1

Skill question

Data set $A$ has the five-number summary: $min = 2, Q_{1} = 5, median = 8, Q_{3} = 10, max = 20$ . Data set $B$ has the five-number summary: $min = 3, Q_{1} = 6, median = 9, Q_{3} = 12, max = 15$ .

Compare the median, range, and interquartile range (IQR) of sets $A$ and $B$ . State which set has the higher median, greater range, and larger IQR.

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Question 2

Skill question

Data set $A$ has a five-number summary: $min = 10$ , $Q_{1} = 12$ , $median = 15$ , $Q_{3} = 18$ , $max = 20$ .

If the maximum value in data set $A$ increases from $20$ to $25$ , calculate the new range and comment on how the $IQR$ is affected.

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Question 3

Skill question

Data set A has a five-number summary: $min = 1$ , $Q_{1} = 2$ , $median = 5$ , $Q_{3} = 8$ , $max = 9$ .

Data set B has a five-number summary: $min = 0$ , $Q_{1} = 3$ , $median = 6$ , $Q_{3} = 7$ , $max = 10$ .

Based on the positions of the median within the quartiles and whiskers, determine the skewness of each data set.

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Question 4

Skill question

Data set $A$ has the following five-number summary: $min = 2$ , $Q_{1} = 5$ , $median = 8$ , $Q_{3} = 10$ , $max = 20$ .

Identify any outliers in data set $A$ using the $1.5 \times IQR$ rule.

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Question 5

Skill question

Data set $A$ has the five-number summary $min = 4$ , $Q_{1} = 7$ , $median = 9$ , $Q_{3} = 13$ , $max = 16$ .

Data set $B$ has the five-number summary $min = 3$ , $Q_{1} = 6$ , $median = 10$ , $Q_{3} = 15$ , $max = 20$ .

Determine which data set has the larger range.

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Question 6

Skill question

Data set $A$ has the following five-number summary: $min = 3, Q_{1} = 5, median = 6, Q_{3} = 7, max = 8$ .

Data set $B$ has the following five-number summary: $min = 8, Q_{1} = 10, median = 12, Q_{3} = 14, max = 16$ .

Every value in data set $B$ is decreased by 3. Determine the new five-number summary of data set $B$ .

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Question 7

Skill question

Data set $A$ has five-number summary $min = 4$ , $Q_{1} = 7$ , $median = 9$ , $Q_{3} = 13$ , $max = 16$ . If every value in data set $A$ is multiplied by 2, determine the new median, $Q_{1}$ , $Q_{3}$ , range, and $IQR$ .

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Question 8

Skill question

Data set A has a five-number summary: $min = 2$ , $Q_{1} = 5$ , $median = 8$ , $Q_{3} = 10$ , $max = 12$ .

Data set B has a five-number summary: $min = 3$ , $Q_{1} = 6$ , $median = 9$ , $Q_{3} = 12$ , $max = 14$ .

Calculate the difference between the medians and interpret which data set has the higher median.

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Question 9

Skill question

Data set $B$ has the following five-number summary: $min = 3$ , $Q_{1} = 6$ , $median = 9$ , $Q_{3} = 12$ , $max = 14$ .

Calculate the lower and upper fences using the $1.5 \times IQR$ rule and determine whether any values would be considered outliers.

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Question 10

Skill question

Two data sets, $A$ and $B$ , have the following quartiles:

Data set $A$ : $Q_{1} = 7$ , $Q_{3} = 13$
Data set $B$ : $Q_{1} = 6$ , $Q_{3} = 15$

Determine which data set has the larger interquartile range ( $IQR$ ).

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Question 11

Skill question

Data set $B$ has five-number summary $min = 8$ , $Q_{1} = 10$ , $median = 12$ , $Q_{3} = 14$ , $max = 16$ . If $3$ is added to every data point in set $B$ , find the new five-number summary.

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Question 12

Skill question

Data set A has five-number summary $min = 10$ , $Q_{1} = 12$ , $median = 15$ , $Q_{3} = 18$ , $max = 20$ . Data set B has $min = 5$ , $Q_{1} = 9$ , $median = 14$ , $Q_{3} = 17$ , $max = 22$ .

Calculate the $IQR$ for both data sets and determine which data set has less variability in the middle $50%$ .

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IB Mathematics Applications & Interpretation Question Type 7: Comparing Two Different Data Sets of Box and Whiskers Exercises