Question

select all the correct answers.

which data sets could be used to create the box plot below?

• 14, 10, 6, 9, 11, 8, 1
• 6, 8, 11, 1, 7, 14, 10
• 7, 9, 11, 1, 6, 7, 14, 8
• 4, 11, 8, 12, 1, 6, 14
• 10, 6, 9, 14, 1, 6, 12, 7

Explanation:

⚡ Using what you learned: displaying data: histograms & box plots

Step 1: Identify the five-number summary from the box plot

From the given box plot, we can read the five-number summary:

• Minimum (\(\text{Min}\)) = \(1\)
• Lower Quartile (\(Q_1\)) = \(6\)
• Median (\(Q_2\)) = \(8\)
• Upper Quartile (\(Q_3\)) = \(11\)
• Maximum (\(\text{Max}\)) = \(14\)

Step 2: Analyze Option 1

Data set: \(14, 10, 6, 9, 11, 8, 1\)

1. Order the data: \(1, 6, 8, 9, 10, 11, 14\)
2. Find the summary statistics:

• \(\text{Min} = 1\)
• \(\text{Max} = 14\)
• \(\text{Median} = 9\) (This does not match the box plot median of \(8\))

Option 1 is incorrect.

Step 3: Analyze Option 2

Data set: \(6, 8, 11, 1, 7, 14, 10\)

1. Order the data: \(1, 6, 7, 8, 10, 11, 14\)
2. Find the summary statistics:

• \(\text{Min} = 1\)
• \(\text{Max} = 14\)
• \(\text{Median} = 8\)
• Lower half: \(1, 6, 7\) \(

ightarrow Q_1 = 6\)

• Upper half: \(10, 11, 14\) \(

ightarrow Q_3 = 11\)

All values match the box plot. Option 2 is correct.

Step 4: Analyze Option 3

Data set: \(7, 9, 11, 1, 6, 7, 14, 8\)

1. Order the data: \(1, 6, 7, 7, 8, 9, 11, 14\)
2. Find the summary statistics:

• \(\text{Min} = 1\)
• \(\text{Max} = 14\)
• \(\text{Median} = \frac{7 + 8}{2} = 7.5\) (This does not match the box plot median of \(8\))

Option 3 is incorrect.

Step 5: Analyze Option 4

Data set: \(4, 11, 8, 12, 1, 6, 14\)

1. Order the data: \(1, 4, 6, 8, 11, 12, 14\)
2. Find the summary statistics:

• \(\text{Min} = 1\)
• \(\text{Max} = 14\)
• \(\text{Median} = 8\)
• Lower half: \(1, 4, 6\) \(

ightarrow Q_1 = 4\) (This does not match \(Q_1 = 6\))

Option 4 is incorrect.

Step 6: Analyze Option 5

Data set: \(10, 6, 9, 14, 1, 6, 12, 7\)

1. Order the data: \(1, 6, 6, 7, 9, 10, 12, 14\)
2. Find the summary statistics:

• \(\text{Min} = 1\)
• \(\text{Max} = 14\)
• \(\text{Median} = \frac{7 + 9}{2} = 8\)
• Lower half: \(1, 6, 6, 7\) \(

ightarrow Q_1 = \frac{6 + 6}{2} = 6\)

• Upper half: \(9, 10, 12, 14\) \(

ightarrow Q_3 = \frac{10 + 12}{2} = 11\)

All values match the box plot. Option 5 is correct.

Answer:

The correct data sets are:

• \(6, 8, 11, 1, 7, 14, 10\) (Second option)
• \(10, 6, 9, 14, 1, 6, 12, 7\) (Fifth option)