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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 3.3.30
Chapter 3, Problem 3.3.30

Boxplots. In Exercises 29–32, use the given data to construct a boxplot and identify the 5-number summary.


Taxis Listed below are times (minutes) of a sample of taxi rides in New York City. The data are from the New York City Taxi and Limousine Commission.
15123131133624

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Step 1: Organize the data in ascending order. The given data is: 15, 12, 31, 3, 11, 33, 62, 4. Arrange it as: 3, 4, 11, 12, 15, 31, 33, 62.
Step 2: Identify the minimum and maximum values. The minimum value is the smallest number in the dataset (3), and the maximum value is the largest number (62).
Step 3: Find the median (Q2). The median is the middle value when the data is ordered. Since there are 8 data points (even number), the median is the average of the 4th and 5th values in the ordered dataset: (12 + 15) / 2.
Step 4: Determine the first quartile (Q1) and third quartile (Q3). Q1 is the median of the lower half of the data (3, 4, 11, 12), and Q3 is the median of the upper half of the data (15, 31, 33, 62).
Step 5: Use the 5-number summary (minimum, Q1, median, Q3, maximum) to construct the boxplot. Plot a box from Q1 to Q3 with a line at the median, and extend whiskers to the minimum and maximum values.

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Key Concepts

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

Boxplot

A boxplot, or box-and-whisker plot, is a graphical representation of a dataset that displays its central tendency and variability. It summarizes data using five key statistics: the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. The box represents the interquartile range (IQR), which contains the middle 50% of the data, while the 'whiskers' extend to the minimum and maximum values, providing a visual overview of the distribution.

Five-number summary

The five-number summary is a descriptive statistic that provides a quick overview of a dataset's distribution. It consists of the minimum value, first quartile (Q1), median (Q2), third quartile (Q3), and maximum value. This summary helps in understanding the spread and center of the data, making it easier to identify outliers and the overall range of the dataset.
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Quartiles

Quartiles are values that divide a dataset into four equal parts, each containing 25% of the data points. The first quartile (Q1) is the median of the lower half of the data, the second quartile (Q2) is the overall median, and the third quartile (Q3) is the median of the upper half. Quartiles are essential for constructing boxplots and understanding the distribution and spread of the data.
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Related Practice
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 range, variance, and standard deviation. Express answers using appropriate units, such as “minutes.”


Earthquakes Use the magnitudes (Richter scale) of the 600 earthquakes listed in Data Set 24 “Earthquakes” in Appendix B. In 1989, the San Francisco Bay Area was struck with an earthquake that measured 7.0 on the Richter scale. If we add that value of 7.0 to those listed in the data set, do the measures of variation change much?

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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.


Weights Use the weights of the males listed in Data Set 2 “ANSUR I 1988,” which were measured in 1988 and use the weights of the males listed in Data Set 3 “ANSUR II 2012,” which were measured in 2012. Does it appear that males have become heavier?

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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.


California Smokers In the California Health Interview Survey, randomly selected adults are interviewed. One of the questions asks how many cigarettes are smoked per day, and results are listed below for 50 randomly selected respondents. How well do the results reflect the smoking behavior of California adults?


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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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