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 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 22m
11. Correlation1h 6m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

3. Describing Data Numerically

Standard Deviation

Statistics

3. Describing Data Numerically

Standard Deviation

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2:28 minutes

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

Verified step by step guidance

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.

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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Textbook Question

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Textbook Question

Comparing Values. In Exercises 13–16, use z scores to compare the given values.

Tallest and Shortest Men The tallest adult male was Robert Wadlow, and his height was 272 cm. The shortest adult male was Chandra Bahadur Dangi, and his height was 54.6 cm. Heights of men have a mean of 174.12 cm and a standard deviation of 7.10 cm. Which of these two men has the height that is more extreme?

Textbook Question

Significant Values. In Exercises 9–12, use the range rule of thumb to identify (a) the values that are significantly low, (b) the values that are significantly high, and (c) the values that are neither significantly low nor significantly high.

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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.

0.48 W/kg

Textbook Question

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

P30

Textbook Question

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

Textbook Question

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

Textbook Question

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

P50

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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

Key Concepts

Percentiles

Data Distribution

Interpreting Radiation Levels

Watch next

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