Question

the northern conference is a running competition where teams from different regions come to compete against each other. the data below represents the number of runners on each cross country team in the northern conference. 12, 15, 15, 17, 19, 19, 20, 22, 24 which box plot correctly summarizes the data? choose 1 answer:

Explanation:

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

The data set is \(12,15,15,17,19,19,20,22,24\).

• Minimum value: \(12\)
• Maximum value: \(24\)
• The median (\(Q2\)): Since \(n = 9\) (odd), the median is the \(\frac{n + 1}{2}\) - th value. \(\frac{9+1}{2}=5\) - th value. So \(Q2=19\)
• For \(Q1\) (lower quartile): Consider the first \(4\) values \(12,15,15,17\). Since \(n = 4\) (even), \(Q1=\frac{15 + 15}{2}=15\)
• For \(Q3\) (upper quartile): Consider the last \(4\) values \(20,22,24\). Since \(n = 4\) (even), \(Q3=\frac{20+22}{2}=21\)

Step2: Analyze the box - plot structure

A box - plot has a box from \(Q1\) to \(Q3\) with a line at \(Q2\) and whiskers from the minimum to the maximum.

• The box should start at \(15\) (\(Q1\)), end at \(21\) (\(Q3\)) and have a line at \(19\) (\(Q2\)). The whiskers should start at \(12\) (minimum) and end at \(24\) (maximum)

Answer:

A. Option Text