Table of contents
- 1. Intro to Stats and Collecting Data55m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically1h 45m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables2h 33m
- 6. Normal Distribution and Continuous Random Variables1h 38m
- 7. Sampling Distributions & Confidence Intervals: Mean1h 3m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- 9. Hypothesis Testing for One Sample1h 1m
- 10. Hypothesis Testing for Two Samples2h 8m
- 11. Correlation48m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 20m
- 14. ANOVA1h 0m
3. Describing Data Numerically
Standard Deviation
Problem 3.3.18
Textbook Question
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


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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