Problem

The graduation rates of several large state schools are shown below. Find the following. \[ \begin{array}{|l|lllllllllll|l|l|l} 56.8 & 60.5 & 68.5 & 70.4 & 75.3 & 75.3 & 60.3 & 64.4 & 77.9 & 83.1 & 40.0 & 40.9 & 48.1 & 56.5 \end{array} \] Send data to Excel Part: $0 / 2$ Part 1 of 2 Identify the five-number summary. Round your answers to two decimal places as needed. \[ \text { Low }=4, Q_{1}=\square, \mathrm{MD}=\square, Q_{3}=\square, \text { High }= \]

Solution

Step 1 :First, sort the data in ascending order: \(40.0, 40.9, 48.1, 56.5, 56.8, 60.3, 60.5, 64.4, 68.5, 70.4, 75.3, 75.3, 77.9, 83.1\)

Step 2 :Lowest value (Low) is \(40.0\)

Step 3 :Highest value (High) is \(83.1\)

Step 4 :To find \(Q_1\), we find the median of the lower half: \(40.0, 40.9, 48.1, 56.5, 56.8, 60.3, 60.5\). The median is \(56.5\)

Step 5 :To find \(Q_3\), we find the median of the upper half: \(64.4, 68.5, 70.4, 75.3, 75.3, 77.9, 83.1\). The median is \(75.3\)

Step 6 :The overall median (MD) is the median of the entire data set: \(56.8, 60.3, 60.5, 64.4, 68.5, 70.4, 75.3\). The median is \(64.4\)

Step 7 :The five-number summary is: \(\text{Low}=40.0, Q_1=56.5, \mathrm{MD}=64.4, Q_3=75.3, \text{High}=83.1\)

Step 8 :\boxed{\text{Low}=40.0, Q_1=56.5, \mathrm{MD}=64.4, Q_3=75.3, \text{High}=83.1}

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Source: https://solvelyapp.com/problems/15508/

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