In Exercises 21–24, find the mean and median for each of the t...

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

Accepted Answer

Hi, everyone. Let's take a look at this practice problem. This problem says a sample of heart rate measurements, beats per minute, or BPM, was collected, where each of 10 individuals has both resting heart rate and active heart rate recorded. The resting heart rate is measured when the person is at rest, while the active heart rate is measured after mild physical activity. For the resting heart rate, we have the values of 62, 72, 88, 58, 90, 66, 64, 80, 70, and 68. And for active heart rate, we have the values of 98, 110, 140, 85, 150, 102, 94, 120, 108, and 100. Are the measures of center the best statistics to use with these data? What other statistical measures might be more appropriate? And we're given 4 possible choices as our answers. For choice A, we have no. The measures of center are not the best. The standard deviation better captures heart rate variability. For choice B, we have, yes, the measures of center are sufficient because the mean and median clearly represent the data. For choice C, it depends. Measures of center are best for resting rates, but variance is better for active rates. And for choice D we have no, the measures of center are not the best, the percentile better captures heart rate variability. Now, we need to answer two different questions for this problem. For the first part, we need to determine if the measures center are the best statistics to use with this data. And we call that the measures at the center are going to be our median and mean. And neither of those quantities give us any information about the variation in our data. And if we look at our resting heart rate data as well as our active heart rate data, we see that there is quite a bit of variation in those values. So that means that the measures of center are not going to be the best statistics to use with this data. So we need to determine for the second part of this question, what other statistical measures might be more appropriate. So we're going to list a few. So the first one that we're going to look at is going to be the standard deviation. Now recall for the standard deviation. That it shows how much individual heart rates are going to deviate from the average, which is going to be helpful to understand the spread in the data. Another quantity to look at is going to be the variance. And recall that the variance is related to the standard deviation. However, it's less intuitive for decision making and harder to interpret. Since it has squared units. Another possible statistical measure is going to be the interquartile range. And recall for the interquartile range. That this measures the spread of the middle 50% of the data, but it doesn't account for the full variation across all individuals. And the final quantity that we'll look at are percentiles. And recall 4th percentiles. That they show the position of a specific value in the data, but they don't provide an overall sense of variability. So, the only possibility that is easy to interpret and gives us a sense of variability across all the data is going to be the standard deviation. So that's gonna be the um statistical measure that we'd find to be the most appropriate for this set of data. So now if we take all this into account and look at our answer choices, the correct answer choice corresponds to answer choice A, which says no, the measures of center are not the best. The standard deviation better captures heart rate variability. So I hope that this explanation has been useful, and I'll see you in the next video.

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Key Concepts

Mean

Median

Measures of Center

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