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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2:35 minutes

Problem 3.3.21

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

Verified step by step guidance

Step 1: Arrange the data in ascending order. The data provided in the image is already sorted in ascending order, so no further action is needed for this step.

Step 2: Determine the position of the 30th percentile (P30) using the formula:

P = \frac{k \times n}{100}

, where

k

is the percentile (30 in this case) and

n

is the total number of data points.

Step 3: Count the total number of data points in the dataset. From the image, there are 40 data points.

Step 4: Calculate the position of P30 using the formula. Substitute

k

= 30 and

n

= 40 into the formula to find the position.

Step 5: Locate the value corresponding to the calculated position in the sorted dataset. If the position is not an integer, interpolate between the two closest values.

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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 30th percentile (P30) is the value below which 30% of the data points lie. To find a specific percentile, the data must be ordered from least to greatest, and then the appropriate position can be calculated using the formula: P = (n + 1) * (percentile/100), where n is the number of data points.

Quartiles

Quartiles are specific percentiles that divide a dataset into four equal parts. The first quartile (Q1) represents the 25th percentile, the second quartile (Q2) is the median or 50th percentile, and the third quartile (Q3) is the 75th percentile. Quartiles help summarize the distribution of data and are useful for identifying outliers and understanding the spread of the dataset.

Data Ordering

Data ordering is the process of arranging data points in a specific sequence, typically from smallest to largest. This step is crucial for calculating percentiles and quartiles, as it allows for accurate identification of the position of values within the dataset. Properly ordered data ensures that statistical measures reflect the true distribution and characteristics of the data being analyzed.

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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

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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

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

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

Textbook Question

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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

Key Concepts

Percentiles

Quartiles

Data Ordering

Watch next

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