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Ch. 3 - Describing, Exploring, and Comparing Data
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoTriola 14th EditionCh. 3 - Describing, Exploring, and Comparing DataProblema 3.3.7a
Capitolo 3, Problema 3.3.7a

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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Step 1: Understand the problem. We are tasked with finding the difference between a specific commute time (95.0 minutes) and the mean commute time (42.6 minutes). This is a straightforward subtraction problem.
Step 2: Write the formula for the difference. The difference can be expressed as: Difference = X - μ, where X is the specific commute time (95.0 minutes) and μ is the mean commute time (42.6 minutes).
Step 3: Substitute the given values into the formula. Replace X with 95.0 and μ with 42.6 in the formula: Difference = 95.0 - 42.6.
Step 4: Perform the subtraction operation to find the difference. This will give you the numerical value of how much the specific commute time deviates from the mean commute time.
Step 5: Interpret the result. The difference represents how many minutes the specific commute time (95.0 minutes) is above the mean commute time (42.6 minutes).

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Z-Score

A Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. It is calculated by subtracting the mean from the value and then dividing by the standard deviation. This standardizes scores on a common scale, allowing for comparison across different datasets.
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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. In the context of the commute times, the mean represents the typical commute duration, providing a baseline for comparison with individual commute times.
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Calculating the Mean

Standard Deviation

Standard deviation is a statistic that quantifies the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range. It is crucial for understanding how individual commute times relate to the average.
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Calculating Standard Deviation
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Sugar Listed below are measured weights (mg) of sugar in Domino packets labelled as containing 3500 mg (or 3.5 g).


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d. Given that the weights are from Domino sugar packets selected from a much larger population, are the weights a sample or a population?

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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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Boxplot Using the same differences from Exercise 1, construct a boxplot and include the values of the 5-number summary.

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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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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?

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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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