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Ch. 3 - Describing, Exploring, and Comparing Data
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446당신이 사용하는 게 아니라요?교과서 변경
3장, 문제 3.3.17

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.


0.48 W/kg

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1
Step 1: Arrange the given radiation levels in ascending order. This step is already completed as the data provided is sorted.
Step 2: Identify the position of the given radiation level (0.48 W/kg) in the sorted list. Count the number of values less than or equal to 0.48.
Step 3: Use the formula for calculating the percentile: \( P = \frac{k}{n} \times 100 \), where \( k \) is the number of values less than or equal to the given value, and \( n \) is the total number of values in the dataset.
Step 4: Substitute \( k \) (the count from Step 2) and \( n \) (the total number of values, which is 50) into the formula.
Step 5: Simplify the formula to find the percentile corresponding to the radiation level of 0.48 W/kg.

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주요 개념

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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 helps in 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 crucial for accurately calculating percentiles and making statistical inferences.
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Visualizing Qualitative vs. Quantitative Data

Interpreting Radiation Levels

In the context of this question, interpreting radiation levels involves understanding the significance of the measured values (in W/kg) and their implications for health and safety. Knowing how to analyze these levels in relation to percentiles allows for assessing how a specific phone's radiation compares to others, which is essential for making informed decisions regarding exposure.
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가이드 코스
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Introduction to Confidence Intervals
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