A sample of blood pressure measurements is taken from a data set and those values $(\mathrm{mm} \mathrm{Hg})$ are listed below. The values are matched so that subjects each have systolic and diastolic measurements. Find the mean and median for each of the two samples and then compare the two sets of results. Are the measures of center the best statistics to use with these data? What else might be better? $\begin{array}{lrrrrrrrrrr} & & & & & & & 106 \\ \text { Systolic: } & 135 & 131 & 118 & 125 & 96 & 103 & 151 & 146 & 99 & 106 \\ \text { Diastolic: } & 84 & 81 & 86 & 58 & 88 & 60 & 71 & 51 & 72 & 53\end{array}$ Find the means. The mean for systolic is $\square \mathrm{mm} \mathrm{Hg}$ and the mean for diastolic is $\square \mathrm{mm} \mathrm{Hg}$.
Solution
Step 1 ：Given the systolic measurements are [135, 131, 118, 125, 96, 103, 151, 146, 99, 106] and the diastolic measurements are [84, 81, 86, 58, 88, 60, 71, 51, 72, 53].
Step 2 ：To find the mean of a set of numbers, we add up all the numbers and then divide by the count of numbers. We can do this for both the systolic and diastolic measurements.
Step 3 ：The mean for systolic is calculated as \(\frac{135+131+118+125+96+103+151+146+99+106}{10} = 121.0 \, \mathrm{mm} \, \mathrm{Hg}\).
Step 4 ：The mean for diastolic is calculated as \(\frac{84+81+86+58+88+60+71+51+72+53}{10} = 70.4 \, \mathrm{mm} \, \mathrm{Hg}\).
Step 5 ：Final Answer: The mean for systolic is \(\boxed{121 \, \mathrm{mm} \, \mathrm{Hg}}\) and the mean for diastolic is \(\boxed{70.4 \, \mathrm{mm} \, \mathrm{Hg}}\).
