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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2:39 minutes

Problem 3.3.22

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.

Q1

Verified step by step guidance

Step 1: Understand the problem. The goal is to find Q1, the first quartile, which represents the 25th percentile of the data. This means identifying the value below which 25% of the data falls.

Step 2: Organize the data. The provided list of cell phone radiation levels is already sorted in ascending order, which is necessary for calculating quartiles.

Step 3: Determine the position of Q1 in the sorted data. Use the formula for the position of a quartile: P = (n + 1) * (percentile / 100), where n is the total number of data points. For Q1, the percentile is 25%.

Step 4: Calculate the position using the formula. Substitute the total number of data points (n) into the formula to find the position of Q1. If the position is not an integer, interpolate between the two closest data points.

Step 5: Identify the value corresponding to the calculated position in the sorted data. This value is Q1, the first quartile.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Percentiles

Percentiles are measures that indicate the relative standing of a value within a dataset. Specifically, the nth percentile is the value below which n percent of the data falls. For example, the 25th percentile (Q1) is the value below which 25% of the observations lie, helping to understand the distribution 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 are useful for summarizing data and identifying the spread and center of a dataset.

Data Distribution

Data distribution refers to how values are spread or arranged in a dataset. Understanding the distribution is crucial for interpreting percentiles and quartiles, as it affects the calculation of these measures. A dataset can be normally distributed, skewed, or uniform, which influences the interpretation of statistical measures and the overall analysis.

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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

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.

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.

P50

Textbook Question

Variance of Roller Coaster Speeds The standard deviation of the sample values in Exercise 1 is 43.1 km/h. What is the variance (including units)?

Textbook Question

Roller Coaster z Score A larger sample of 92 roller coaster maximum speeds has a mean of 85.9 km/h and a standard deviation of 28.7 km/h. What is the z score for a speed of 34 km/h? Does the z score suggest that the speed of 34 km/h is significantly low?

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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.Q1

Key Concepts

Percentiles

Quartiles

Data Distribution

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.

Q1