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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 3.3.18
Chapter 3, Problem 3.3.18

Percentiles. In Exercises 17–20, use the following radiation levels (in W/kg) for 50 different cell phones. Find the percentile corresponding to the given radiation level.




1.47 W/kg

Verified step by step guidance
1
Step 1: Organize the data in ascending order. The data provided is already sorted in ascending order, so no further action is needed for this step.
Step 2: Identify the position of the given radiation level (1.47 W/kg) in the sorted data. Count how many values are less than or equal to 1.47 W/kg.
Step 3: Use the formula for the percentile rank: \( P = \frac{k}{n} \times 100 \), where \( k \) is the number of values less than or equal to the given value, and \( n \) is the total number of data points (50 in this case).
Step 4: Substitute the values into the formula. Count \( k \) (the number of values less than or equal to 1.47 W/kg) and substitute \( n = 50 \) into the formula.
Step 5: Simplify the formula to calculate the percentile rank. This will give the percentile corresponding to the radiation level of 1.47 W/kg.

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Key Concepts

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

Percentiles

A percentile is a statistical measure that indicates the value below which a given percentage of observations in a group falls. For example, the 50th percentile (median) is the value that separates the higher half from the lower half of the data set. Understanding percentiles is crucial for interpreting data distributions and comparing individual scores to a larger dataset.

Data Distribution

Data distribution refers to the way in which data points are spread or arranged across different values. It can be visualized using histograms or box plots, and it helps in understanding the central tendency, variability, and overall shape of the data. Recognizing the distribution is essential for accurately calculating percentiles and making informed statistical inferences.
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Interpreting Radiation Levels

In the context of cell phone radiation levels, interpreting these values involves understanding their implications for health and safety. The radiation levels measured in W/kg can be compared against established safety standards. Knowing how to interpret these levels in relation to percentiles allows for assessing how a specific phone's radiation compares to others in the dataset, providing insights into its relative safety.
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Related Practice
Textbook Question

Critical Thinking. For Exercises 5–20, watch out for these little buggers. Each of these exercises involves some feature that is somewhat tricky. Find the (a) mean, (b) median, (c) mode, (d) midrange, and then answer the given question.


Geography Majors The data listed below are estimated incomes (dollars) of students who graduated from the University of North Carolina (UNC) after majoring in geography. The data are based on graduates in the year 1984. The income of basketball superstar Michael Jordan (a 1984 UNC graduate and geography major) is included. Does his income have much of an effect on the measures of center? Based on these data, would the college have been justified by saying that the mean income of a graduate in their geography program is greater than \$250,000?


17,466 18,085 17,875 19,339 19,682 19,610 18,259 16,354 2,200,000

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Textbook Question

Boxplots from Large Data Sets in Appendix B. In Exercises 33–36, use the given data sets in Appendix B. Use the boxplots to compare the two data sets.


Pulse Rates Use the same scale to construct boxplots for the pulse rates of males and females from Data Set 1 “Body Data” in Appendix B.

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Textbook Question

What’s Wrong? Education Week magazine published a list consisting of the mean teacher salary in each of the 50 states for a recent year. If we add the 50 means and then divide by 50, we get \$56,479. Is the value of \$56,479 the mean teacher salary for the population of all teachers in the 50 United States? Why or why not?

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Textbook Question

Identifying Significant Values with the Range Rule of Thumb. In Exercises 33–36, use the range rule of thumb to identify the limits separating values that are significantly low or significantly high.


Foot Lengths Based on Data Set 9 “Foot and Height” in Appendix B, adult males have foot lengths with a mean of 27.32 cm and a standard deviation of 1.29 cm. Is the adult male foot length of 30 cm significantly low, significantly high, or neither? Explain.

Textbook Question

Resistant Measures Listed below are 10 wait times (minutes) for “Rock ‘n’ Roller Coaster” at 10 AM (from Data Set 33 “Disney World Wait Times”). The data are listed in order from lowest to highest. Find the mean and median of these ten values. Then find the mean and median after excluding the value of 180, which appears to be an outlier. Compare the two sets of results. How much was the mean affected by the inclusion of the outlier? How much is the median affected by the inclusion of the outlier?


15 20 25 30 30 35 45 50 50 180 

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Textbook Question

In Exercises 29–32, compute the mean of the data summarized in the frequency distribution. Also, compare the computed means to the actual means obtained by using the original list of data values, which are as follows: (29) 31.4 minutes; (Exercise 30) 140.6 minutes; (Exercise 31) 55.2 years; (Exercise 32) 240.2 seconds.


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