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 construct a boxplot and identify the 5 - number summary.
121 125 135 130 120 125 129 130 147 120 127 140 149 150
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

Sort the given data in ascending order:
$$120, 120, 121, 125, 125, 127, 129, 130, 130, 135, 140, 147, 149, 150$$

Step2: Find the minimum value

The minimum value ($Q_0$) is the first value in the sorted list.
$$Q_0 = 120$$

Step3: Find the first quartile ($Q_1$)

For $n = 14$ (even number of data points), the lower half of the data is the first $n/2=7$ values: $120, 120, 121, 125, 125, 127, 129$.
The median of the lower - half (first quartile) is the 4th value.
$$Q_1 = 125$$

Step4: Find the median ($Q_2$)

For $n = 14$ (even number of data points), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th values.
The $\frac{n}{2}=7$th value is $129$ and the $(\frac{n}{2}+1) = 8$th value is $130$.
$$Q_2=\frac{129 + 130}{2}=129.5$$

Step5: Find the third quartile ($Q_3$)

The upper half of the data is the last $n/2 = 7$ values: $130, 135, 140, 147, 149, 150$.
The median of the upper - half (third quartile) is the 4th value of the upper - half.
$$Q_3=140$$

Step6: Find the maximum value

The maximum value ($Q_4$) is the last value in the sorted list.
$$Q_4 = 150$$

Answer:

The 5 - number summary is $120$, $125$, $129.5$, $140$, and $150$ all in mm Hg.