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Ch. 3 - Describing, Exploring, and Comparing Data
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 3 - Describing, Exploring, and Comparing DataProblem 3.1.21
Chapter 3, Problem 3.1.21

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

Verified step by step guidance
1
Step 1: Calculate the mean for each sample. The mean is the average of the data points and is calculated using the formula: Mean=∑xn, where x represents each data point and n is the total number of data points. Perform this calculation separately for the systolic and diastolic measurements.
Step 2: Calculate the median for each sample. The median is the middle value when the data points are arranged in ascending order. If the number of data points is odd, the median is the middle value. If the number of data points is even, the median is the average of the two middle values. Arrange the systolic and diastolic measurements in ascending order and find their respective medians.
Step 3: Compare the mean and median for each sample. Analyze whether the mean and median are close to each other or if there is a significant difference. This comparison can help identify whether the data distribution is symmetric or skewed.
Step 4: Evaluate whether the measures of center (mean and median) are the best statistics to use for these data. Consider factors such as the presence of outliers or skewness in the data. If the data contains outliers or is heavily skewed, the median might be a better measure of center than the mean.
Step 5: Suggest alternative statistics or methods if the measures of center are not ideal. For example, consider using the trimmed mean (which excludes extreme values) or analyzing the data using measures of spread such as the interquartile range (IQR) or standard deviation to better understand the variability in the data.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Mean

The mean, or average, is calculated by summing all values in a dataset and dividing by the number of values. It provides a central value that represents the dataset, but can be influenced by extreme values (outliers). In the context of blood pressure measurements, calculating the mean for both systolic and diastolic values will help summarize the overall blood pressure levels of the subjects.
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Median

The median is the middle value of a dataset when arranged in ascending order. If there is an even number of observations, the median is the average of the two middle values. It is a robust measure of center that is less affected by outliers, making it particularly useful for skewed distributions, such as blood pressure data that may have extreme values.
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Measures of Center

Measures of center, including the mean and median, are statistical tools used to summarize a dataset with a single representative value. While the mean provides a mathematical average, the median offers a positional average that can be more informative in certain contexts. In analyzing blood pressure data, it is important to consider whether these measures adequately represent the data's distribution or if additional statistics, like mode or range, might provide better insights.
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Related Practice
Textbook Question

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Textbook Question

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P30


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Textbook Question

In Exercises 5–20, find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 3-1, where we found measures of center. Here we find measures of variation.) Then answer the given questions.


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12 26 46 15 11 87 77 62 60 69 61

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Textbook Question

Large Data Sets from Appendix B. In Exercises 25–28, refer to the indicated data set in Appendix B. Use software or a calculator to find the means and medians.


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Textbook Question

In Exercises 5–20, find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 3-1, where we found measures of center. Here we find measures of variation.) Then answer the given questions.


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Textbook Question

Weighted Mean A student of the author earned grades of 63, 91, 88, 84, and 79 on her five regular statistics tests. She earned grades of 86 on the final exam and 90 on her class projects. Her combined homework grade was 70. The five regular tests count for 60% of the final grade, the final exam counts for 10%, the project counts for 15%, and homework counts for 15%. What is her weighted mean grade? What letter grade did she earn (A, B, C, D, or F)? Assume that a mean of 90 or above is an A, a mean of 80 to 89 is a B, and so on.

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