Question

fourteen different second - year medical students at a hospital measured the blood pressure of the same person. the systolic readings (mm hg) are listed below. use the given data to construct a boxplot and identify the 5 - number summary.
132 128 135 131 120 125 139 130 149 125 143 140 149 150
the 5 - number summary is □,□,□,□, and □, all in mm hg.
(use ascending order. type integers or decimals. do not round.)

Explanation:

Step1: Sort the data

First, sort the data in ascending order.
\(120, 125, 125, 128, 130, 131, 132, 135, 139, 140, 143, 149, 149, 150\)

Step2: Find the minimum

The minimum value is the first value in the sorted list.
\(Min = 120\)

Step3: Find the first quartile (\(Q_1\))

For \(n = 14\) (number of data points), the position of \(Q_1\) is \(\frac{n + 1}{4}=\frac{14+1}{4}=3.75\).
\(Q_1=125+(128 - 125)\times0.75=125 + 2.25=127.25\)

Step4: Find the median (\(Q_2\))

The position of the median for \(n = 14\) is \(\frac{n}{2}=7\) and \(\frac{n}{2}+1 = 8\).
\(Q_2=\frac{132 + 135}{2}=133.5\)

Step5: Find the third quartile (\(Q_3\))

The position of \(Q_3\) is \(\frac{3(n + 1)}{4}=\frac{3\times(14 + 1)}{4}=11.25\)
\(Q_3=143+(149 - 143)\times0.25=143+1.5 = 144.5\)

Step6: Find the maximum

The maximum value is the last value in the sorted list.
\(Max=150\)

Answer:

\(120,127.25,133.5,144.5,150\)