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: 136 145 99 100 140 134 155 122 111 151 diastolic: 76 66 80 65 69 58 85 51 77 54 find the medians. the median for systolic is 135 mm hg and the median for diastolic is 67.5 mm hg. (type integers or decimals rounded to one decimal place as needed.) compare the results. choose the correct answer below. a. the median is lower for the diastolic pressure, but the mean is lower for the systolic pressure. b. the mean and the median for the diastolic pressure are both lower than the mean and the median for the systolic pressure. c. the mean and median appear to be roughly the same for both types of blood pressure. d. the mean and the median for the systolic pressure are both lower than the mean and the median for the diastolic pressure. e. the mean is lower for the diastolic pressure, but the median is lower for the systolic pressure.

Explanation:

Step1: Recall the definitions of mean and median

The mean is the sum of all data - points divided by the number of data - points. The median is the middle value when the data is arranged in ascending or descending order. If there are \(n\) data - points and \(n\) is even, the median is the average of the two middle values.

Step2: Analyze the given statement about systolic and diastolic blood - pressure medians

We are given that the median for systolic is \(135\) mm Hg and for diastolic is \(67.5\) mm Hg. We need to compare the mean and median for each type of blood - pressure.

Step3: Analyze option A

If the median is lower for diastolic pressure and the mean is lower for systolic pressure, we need to check if this is consistent with the properties of mean and median. In a left - skewed distribution, the mean is less than the median, and in a right - skewed distribution, the mean is greater than the median. However, without calculating the means, we can't be sure. But based on the given information about medians, option A is incorrect.

Step4: Analyze option B

If the mean and median for diastolic pressure are both lower than for systolic pressure, we need to consider the nature of the data. Since we know the medians (\(135\) for systolic and \(67.5\) for diastolic), and we know that the mean is affected by extreme values. If the data for systolic pressure has larger values on average (as indicated by the higher median), it is likely that the mean of systolic pressure is also higher. This option is consistent with the given median values.

Step5: Analyze option C

If the mean and median appear to be roughly the same for both types of blood - pressure, this is not consistent with the given median values (\(135\) for systolic and \(67.5\) for diastolic). So, this option is incorrect.

Step6: Analyze option D

If the mean and the median for systolic pressure are both lower than the mean and median for diastolic pressure, this is contrary to the given median values. So, this option is incorrect.

Step7: Analyze option E

If the mean is lower for diastolic pressure but the median is lower for systolic pressure, this is not consistent with the given median values. So, this option is incorrect.

Answer:

B. The mean and the median for the diastolic pressure are both lower than the mean and the median for the systolic pressure.