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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 3.3.23
Chapter 3, Problem 3.3.23

In Exercises 21–28, use the same list of cell phone radiation levels given for Exercises 17–20. Find the indicated percentile or quartile.


Q3


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Step 1: Arrange the data in ascending order. The data provided in the image is already sorted in ascending order.
Step 2: Determine the position of Q3 (the third quartile). Q3 corresponds to the 75th percentile, which can be calculated using the formula: P=kn×N, where k = 75, n = 100 (percentile scale), and N = total number of data points.
Step 3: Calculate the position of Q3 using the formula. If the position is not an integer, round up to the nearest whole number to find the rank of the data point corresponding to Q3.
Step 4: Locate the value in the sorted data set that corresponds to the calculated position. This value represents Q3.
Step 5: Interpret the result. Q3 divides the data set such that 75% of the values are below it and 25% are above it.

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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 measure used in statistics to indicate the value below which a given percentage of observations fall. For example, the 25th percentile (Q1) is the value below which 25% of the data points lie. Understanding percentiles helps in interpreting the distribution of data and comparing individual scores to a larger dataset.

Quartiles

Quartiles are specific percentiles that divide a dataset into four equal parts. The first quartile (Q1) marks the 25th percentile, the second quartile (Q2) is the median or 50th percentile, and the third quartile (Q3) is the 75th percentile. Quartiles provide insights into the spread and center of the data, making them essential for descriptive statistics.
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Data Distribution

Data distribution refers to how values are spread or arranged in a dataset. It can be visualized through graphs like histograms or box plots, which help identify patterns such as skewness or outliers. Understanding the distribution is crucial for accurately calculating percentiles and quartiles, as these measures depend on the arrangement of data points.
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Related Practice
Textbook Question

Finding Standard Deviation from a Frequency Distribution. In Exercises 37–40, refer to the frequency distribution in the given exercise and compute the standard deviation by using the formula below, where x represents the class midpoint, f represents the class frequency, and n represents the total number of sample values. Also, compare the computed standard deviations to these standard deviations obtained by using Formula 3-4 with the original list of data values: (Exercise 37) 18.5 minutes; (Exercise 38) 36.7 minutes; (Exercise 39) 6.9 years; (Exercise 40) 20.4 seconds.


Standard deviation for frequency distribution



Textbook Question

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Textbook Question

Finding Standard Deviation from a Frequency Distribution. In Exercises 37–40, refer to the frequency distribution in the given exercise and compute the standard deviation by using the formula below, where x represents the class midpoint, f represents the class frequency, and n represents the total number of sample values. Also, compare the computed standard deviations to these standard deviations obtained by using Formula 3-4 with the original list of data values: (Exercise 37) 18.5 minutes; (Exercise 38) 36.7 minutes; (Exercise 39) 6.9 years; (Exercise 40) 20.4 seconds.


Standard deviation for frequency distribution


Textbook Question

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138 130 135 140 120 125 120 130 130 144 143 140 130 150

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Textbook Question

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Textbook Question

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