Question

2 choose the set of data that is displayed in the box plot. data set a: 1, 30, 39, 12, 13, 20, 11, 22, 29 data set b: 11, 28, 13, 1, 11, 39, 30, 20, 22 data set a data set b

Explanation:

Step1: Sort data sets

Sort Data set A: \(1, 11, 12, 13, 20, 22, 29, 30, 39\)
Sort Data set B: \(1, 11, 11, 13, 20, 22, 28, 30, 39\)

Step2: Find five - number summary

For a box - plot, we need the minimum, first quartile (\(Q_1\)), median (\(Q_2\)), third quartile (\(Q_3\)), and maximum.

• For sorted Data set A:
• Minimum \(=1\)
• \(n = 9\), median position \(=\frac{n + 1}{2}=5\), so median \(=20\)
• Lower half: \(1, 11, 12, 13\), \(Q_1=\frac{11 + 12}{2}=11.5\) (not \(11\))
• For sorted Data set B:
• Minimum \(=1\)
• \(n = 9\), median position \(=\frac{n+1}{2}=5\), median \(=20\)
• Lower half: \(1, 11, 11, 13\), \(Q_1 = 11\)
• Upper half: \(22, 28, 30, 39\), \(Q_3=29\)
• Maximum \(=39\)

Answer:

Data set B