Question

In Exercises 21–24, find the mean and median for each of the two samples, then compare the two sets of results.

Blood Pressure A sample of blood pressure measurements is taken from Data Set 1 “Body Data” in Appendix B, and those values (mm Hg) are listed below. The values are matched so that 10 subjects each have systolic and diastolic measurements. (Systolic is a measure of the

force of blood being pushed through arteries, but diastolic is a measure of blood pressure when the heart is at rest between beats.) Are the measures of center the best statistics to use with these data? What else might be better?

Systolic: 118 128 158 96 156 122 116 136 126 120

Diastolic: 80 76 74 52 90 88 58 64 72 82

Short answer

The mean values for systolic and diastolic measurements are 127.6 mmHg and 73.6mmHg, respectively.

The median values for systolic and diastolic measurements are124.0mmHg and 75.0 mmHg, respectively.

No, mean and median are not appropriate statistics in the study as the data is paired. Correlation analysis would be better.

Step-by-step solution

Given information

The paired data for systolic and diastolic measures of 10 subjects are listed.

Systolic	118	128	158	96	156	122	116	136	126	120
Diastolic	80	76	74	52	90	88	58	64	72	82

Compute mean for each data set

The mean is computed as:

$\overline{x}=\frac{\sum x}{n}$, where xis the observations andnis the count of the observations.

Substitute the values for systolic measurements.

$$\begin{gathered} {\overline{x}}_S=\frac{118+128+158+...+120}{10} \\ =\frac{1276}{10} \\ \approx 127.6 \end{gathered}$$

Substitute the values for diastolic measurements.

$$\begin{gathered} {\overline{x}}_D=\frac{80+76+74+...+82}{10} \\ =\frac{736}{10} \\ =73.6 \end{gathered}$$

Thus, the mean values for systolic and diastolic blood pressure measurements are 127.6 mmHg and 73.6 mmHg, respectively.

Compute the median for each set of measurements

The steps to compute median:

• The measurements need to be sorted.
• If n is even, the median is the average of the two middle values.
• If n is odd, the median is the middle value.

Compute the median for systolic measurements.

The number of observations is 10.

Arrange the observations in ascending order.

96
116
118
120
122
126
128
136
156
158

The middlemost observations are 122 and 126.

The median is given as:

$$\begin{gathered} M=\frac{122+126}{2} \\ =\frac{248}{2} \\ =124 \end{gathered}$$

Thus, the median for systolic measurements is 124.0 mmHg.

Compute the median for diastolic measurements.

The number of observations is 10.

Arrange the observations in ascending order.

52
58
64
72
74
76
80
82
88
90

The middlemost observations are 74 and 76.

The median is given as:

$$\begin{gathered} M=\frac{74+76}{2} \\ =\frac{150}{2} \\ =75 \end{gathered}$$

Thus, the median for diastolic measurements is 75.0 mmHg.

Summarize the results and express the best statistics for the data

The summarized results are:

Measures	Systolic	Diastolic
Mean	127.6 mm Hg	73.6 mmHg
Median	124.0 mmHg	75.0 mmHg

The measures of the center; mean, and median are computed for each of the two groups of data. The data is paired; that is, a pair of observations is obtained from one subject.

The mean and median values computed individually cannot be appropriately interpreted. Moreover, the comparison between the two measures would not provide any apt conclusion about the study.

Since the data is paired, a simultaneous study like correlation analysis can be highly useful, which would help to understand the change in one variable caused by a change in the other.