Question

a sample of blood pressure measurements is taken from a data set and those values (mm 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?
systolic: 114, 96, 146, 109, 121, 139, 97, 137, 117, 118
diastolic: 57, 74, 59, 56, 67, 58, 91, 69, 54, 76
find the means.
the mean for systolic is 119.4 mm hg and the mean for diastolic is 66.1 mm hg.
(type integers or decimals rounded to one decimal place as needed.)
find the medians.
the median for systolic is □ mm hg and the median for diastolic is □ mm hg.
(type integers or decimals rounded to one decimal place as needed.)

Explanation:

Step1: List Systolic Data

Systolic values: 114, 96, 146, 109, 121, 139, 97, 137, 117, 118
Sort them: 96, 97, 109, 114, 117, 118, 121, 137, 139, 146
Number of data points \( n = 10 \) (even), so median is average of \( \frac{n}{2} \)-th and \( (\frac{n}{2}+1) \)-th terms.
\( \frac{n}{2} = 5 \), \( \frac{n}{2}+1 = 6 \)
5th term: 117, 6th term: 118
Median (systolic) \( = \frac{117 + 118}{2} = \frac{235}{2} = 117.5 \)

Step2: List Diastolic Data

Diastolic values: 57, 74, 59, 56, 67, 58, 91, 69, 54, 76
Sort them: 54, 56, 57, 58, 59, 67, 69, 74, 76, 91
Number of data points \( n = 10 \) (even), median is average of \( \frac{n}{2} \)-th and \( (\frac{n}{2}+1) \)-th terms.
\( \frac{n}{2} = 5 \), \( \frac{n}{2}+1 = 6 \)
5th term: 59, 6th term: 67
Median (diastolic) \( = \frac{59 + 67}{2} = \frac{126}{2} = 63.0 \)

Answer:

The median for systolic is \( 117.5 \) mm Hg and the median for diastolic is \( 63.0 \) mm Hg.