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

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

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.

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.

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.

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.

The summarized results are:

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.