Textbook Question
Archaeology The depths (in inches) at which 10 artifacts are found are listed.
20.7 24.8 30.5 26.2 36.0 34.3 30.3 29.5 27.0 38.5
a. Find the range of the data set.
Ch. 2 - Descriptive Statistics
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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Table of contents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
Chapter 2, Problem 2.5.17a
Drawing a Box-and-Whisker Plot In Exercises 15–18,
(a) find the five-number summary
4 7 7 5 2 9 7 6 8 5 8 4 1 5 2 8 7 6 6 9
Verified step by step guidance1
Step 1: Organize the data set in ascending order. The given data set is: 1, 2, 2, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9.
Step 2: Identify the minimum value (smallest number in the data set) and the maximum value (largest number in the data set).
Step 3: Find the median (Q2), which is the middle value of the data set. If the data set has an even number of values, the median is the average of the two middle numbers.
Step 4: Determine the first quartile (Q1), which is the median of the lower half of the data (excluding the overall median). Similarly, find the third quartile (Q3), which is the median of the upper half of the data.
Step 5: Use the five-number summary (minimum, Q1, median, Q3, maximum) to construct the box-and-whisker plot. The box represents Q1 to Q3, with a line at the median, and the whiskers extend to the minimum and maximum values.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Five-Number Summary
The five-number summary is a descriptive statistic that provides a quick overview of a dataset. It consists of the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values. This summary helps in understanding the distribution and spread of the data, making it easier to identify outliers and the overall range.
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Box-and-Whisker Plot
A box-and-whisker plot, or box plot, visually represents the five-number summary of a dataset. It displays the minimum and maximum values as 'whiskers' and the quartiles as a 'box' in the middle. This plot is useful for comparing distributions between different datasets and identifying potential outliers.
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Quartiles
Quartiles are values that divide a dataset into four equal parts, each containing 25% of the data points. The first quartile (Q1) is the median of the lower half of the data, the second quartile (Q2) is the overall median, and the third quartile (Q3) is the median of the upper half. Understanding quartiles is essential for interpreting the spread and central tendency of the data.
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Related Practice
Textbook Question
Using the Empirical Rule In Exercises 29–34, use the Empirical Rule.
Use the sample statistics from Exercise 29 and assume the number of vehicles in the sample is 75.
a. Estimate the number of vehicles whose speeds are between 63 miles per hour and 71 miles per hour.
Textbook Question
Protein Powder During a quality assurance check, the actual contents (in grams) of six containers of protein powder were recorded as 1525, 1526, 1502, 1516, 1529, and 1511.
a. Find the mean and the median of the contents.
Textbook Question
Yoga Classes The data sets at the left show the ages of all participants in two yoga classes.
a. Make a back-to-back stem-and-leaf plot as described in Exercise 41 to display the data.
Textbook Question
Extending Concepts
Data Analysis Students in an experimental psychology class did research on depression as a sign of stress. A test was administered to a sample of 30 students. The scores are shown in the table at the left.
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a. Find the mean and the median of the data.
Textbook Question
Shifting Data Sample annual salaries (in thousands of dollars) for employees at a company are listed.
40 35 49 53 38 39 40
37 49 34 38 43 47 35
a. Find the sample mean and the sample standard deviation.