Question

a sample of 10 bags of marbles is selected, and the number of marbles in each bag is counted. the list shows the number of marbles in each bag. 22, 24, 13, 19, 19, 23, 22, 18, 20, 23 which box plot best represents the data?

Explanation:

Step1: Sort the data

First, sort the data set \(13,18,19,19,20,22,22,23,23,24\).

Step2: Find the minimum, maximum, median, Q1, and Q3

• Minimum: \(13\)
• Maximum: \(24\)
• Median (\(Q2\)): For \(n = 10\) (even), \(Q2=\frac{20 + 22}{2}=21\)
• First quartile (\(Q1\)): The median of the first \(5\) numbers \(\{13,18,19,19,20\}\), \(Q1 = 19\)
• Third quartile (\(Q3\)): The median of the last \(5\) numbers\(\{22,22,23,23,24\}\), \(Q3=23\)

Answer:

The box - plot with minimum \(13\), \(Q1 = 19\), \(Q2=21\), \(Q3 = 23\), and maximum \(24\) best represents the data.