Question

which box plot represents the data set 1, 1, 3, 3, 3, 7, 9, 9, 9, 9, 15?
a.
0 2 4 6 8 10 12 14 16
b.
0 2 4 6 8 10 12 14 16
c.
0 2 4 6 8 10 12 14 16
d.
0 2 4 6 8 10 12 14 16

Explanation:

Step1: Find the minimum, maximum, median, Q1, Q3

• The data set is \(1,1,3,3,3,7,9,9,9,9,15\)
• Minimum (\(min\)): \(1\)
• Maximum (\(max\)): \(15\)
• Number of data points \(n = 11\)
• Median (\(Q2\)): For \(n = 11\), the median is the \(\frac{n + 1}{2}=6^{th}\) value. So \(Q2=7\)
• First quartile (\(Q1\)): The lower half of the data is \(1,1,3,3,3\). The median of the lower half (for \(n = 5\), \(\frac{n+1}{2}=3^{rd}\) value) is \(Q1 = 3\)
• Third quartile (\(Q3\)): The upper half of the data is \(9,9,9,9,15\). The median of the upper half (for \(n = 5\), \(\frac{n + 1}{2}=3^{rd}\) value) is \(Q3=9\)

Step2: Analyze each option

• Option A: Incorrect as \(Q1

eq2\), \(Q3
eq12\)

• Option B: \(min = 1\), \(Q1 = 1\) (incorrect as \(Q1=3\))
• Option C: \(min = 1\), \(Q1 = 3\), \(Q2=7\), \(Q3=9\), \(max = 15\)
• Option D: \(Q3

eq8\) (incorrect)

Answer:

C.