Textbook Question
Degrees of Freedom Five recent U.S. presidents had a mean age of 56.2 years at the time of their inauguration. Four of these ages are 64, 46, 54, and 47.
a. Find the missing value.
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Ch. 3 - Describing, Exploring, and Comparing Data
Triola14th EditionElementary StatisticsISBN: 9780137366446
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Table of contents
- Ch. 1 - Introduction to Statistics88
- Ch. 2 - Exploring Data with Tables and Graphs70
- Ch. 3 - Describing, Exploring, and Comparing Data66
- Ch. 4 - Probability112
- Ch. 5 - Discrete Probability Distributions109
- Ch. 6 - Normal Probability Distributions122
- Ch. 7 - Estimating Parameters and Determining Sample Sizes107
- Ch. 8 - Hypothesis Testing75
- Ch. 9 - Inferences from Two Samples94
- Ch. 10 - Correlation and Regression80
- Ch. 11 - Goodness-of-Fit and Contingency Tables29
- Ch. 12 - Analysis of Variance42
Chapter 3, Problem 3.3.5a
z Scores. In Exercises 5–8, express all z scores with two decimal places.
Diastolic Blood Pressure of Females For the diastolic blood pressure measurements of females listed in Data Set 1 “Body Data” in Appendix B, the highest measurement is 98 mm Hg. The 147 diastolic blood pressure measurements of females have a mean of 70.2 mm Hg and a standard deviation of 11.2 mm Hg.
a. What is the difference between the highest diastolic blood pressure and the mean of the diastolic blood pressures for females?
Verified step by step guidance1
Step 1: Understand the problem. We are tasked with finding the difference between the highest diastolic blood pressure measurement and the mean diastolic blood pressure for females. This is a straightforward subtraction problem.
Step 2: Identify the given values. From the problem, the highest diastolic blood pressure is 98 mm Hg, the mean diastolic blood pressure is 70.2 mm Hg, and the standard deviation is 11.2 mm Hg (though the standard deviation is not needed for this specific part of the problem).
Step 3: Write the formula for the difference. The difference can be calculated as: , where is the highest diastolic blood pressure and is the mean diastolic blood pressure.
Step 4: Substitute the given values into the formula. Replace with 98 and with 70.2 in the formula: .
Step 5: Perform the subtraction to find the difference. This will give you the numerical value of the difference between the highest diastolic blood pressure and the mean.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Z Scores
A z score, or standard score, indicates how many standard deviations an element is from the mean. It is calculated by subtracting the mean from the value and then dividing by the standard deviation. Z scores are useful for comparing data points from different distributions and understanding their relative position within a dataset.
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Z-Scores From Given Probability - TI-84 (CE) Calculator
Mean
The mean, or average, is a measure of central tendency that is calculated by summing all values in a dataset and dividing by the number of values. It provides a single value that represents the center of the data distribution. In the context of blood pressure measurements, the mean gives an idea of the typical diastolic blood pressure for females in the dataset.
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04:52Calculating the Mean
Standard Deviation
Standard deviation is a statistic that measures the dispersion or spread of a set of values around the mean. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates a wider spread. In this case, the standard deviation of 11.2 mm Hg helps to understand the variability in diastolic blood pressure measurements among females.
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Related Practice
Textbook Question
z Scores. In Exercises 5–8, express all z scores with two decimal places.
Diastolic Blood Pressure of Females For the diastolic blood pressure measurements of females listed in Data Set 1 “Body Data” in Appendix B, the highest measurement is 98 mm Hg. The 147 diastolic blood pressure measurements of females have a mean of 70.2 mm Hg and a standard deviation of 11.2 mm Hg.
b. How many standard deviations is that [the difference found in part (a)]?
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Textbook Question
Boxplot Using the same differences from Exercise 1, construct a boxplot and include the values of the 5-number summary.
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Textbook Question
z Scores. In Exercises 5–8, express all z scores with two decimal places.
New York City Commute Time New York City commute times (minutes) are listed in Data Set 31 “Commute Times” in Appendix B. The 1000 times have a mean of 42.6 minutes and a standard deviation of 26.2 minutes. Consider the commute time of 95.0 minutes.
b. How many standard deviations is that [the difference found in part (a)]?
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Textbook Question
z Scores. In Exercises 5–8, express all z scores with two decimal places.
New York City Commute Time New York City commute times (minutes) are listed in Data Set 31 “Commute Times” in Appendix B. The 1000 times have a mean of 42.6 minutes and a standard deviation of 26.2 minutes. Consider the commute time of 95.0 minutes.
a. What is the difference between the commute time of 95.0 minutes and the mean commute time?
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Textbook Question
Correlation Between Magnitudes and Depths Using the paired magnitude/depth data, construct the graph that is helpful in determining whether there is a correlation between earthquake magnitudes and depths. Based on the result, does there appear to be a correlation?
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