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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2:25 minutes

Problem 3.3.23

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.

Q3

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.

Step 2: Determine the position of Q3 (the third quartile). Q3 corresponds to the 75th percentile, which can be calculated using the formula:

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

, where k = 75, n = 100 (percentile scale), and N = total number of data points.

Step 3: Calculate the position of Q3 using the formula. If the position is not an integer, round up to the nearest whole number to find the rank of the data point corresponding to Q3.

Step 4: Locate the value in the sorted data set that corresponds to the calculated position. This value represents Q3.

Step 5: Interpret the result. Q3 divides the data set such that 75% of the values are below it and 25% are above it.

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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 25th percentile (Q1) is the value below which 25% of the data points lie. Understanding percentiles helps in interpreting the distribution of data and comparing individual scores to a larger dataset.

Quartiles

Quartiles are specific percentiles that divide a dataset into four equal parts. The first quartile (Q1) marks the 25th percentile, the second quartile (Q2) is the median or 50th percentile, and the third quartile (Q3) is the 75th percentile. Quartiles provide insights into the spread and center of the data, making them essential for descriptive statistics.

Data Distribution

Data distribution refers to how values are spread or arranged in a dataset. It can be visualized through graphs like histograms or box plots, which help identify patterns such as skewness or outliers. Understanding the distribution is crucial for accurately calculating percentiles and quartiles, as these measures depend on the arrangement of data points.

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Related Practice

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?

Textbook Question

Estimating s The sample of 92 roller coaster maximum speeds includes values ranging from a low of 10 km/h to a high of 194 km/h. Use the range rule of thumb to estimate the standard deviation.

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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.Q3

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.

Q3