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Chapter 3: Problem 98

Briefly explain what summary measures are used to construct a box-and-whisker plot.

Short Answer

Expert verified
The summary measures used to construct a box-and-whisker plot are minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value. They show the spread and skewness of a dataset visually.

Step by step solution

01

Understanding of Box-and-Whisker Plot

A box-and-whisker plot, also known as a box plot, is a way to show the spread and skewness of a dataset visually. This kind of plot displays the summary of the set of data values inclusive of minimum and maximum values, median, and the first and third quartile.
02

Identifying Components of the Box-and-Whisker Plot

A box-and-whisker plot has several components. The 'box' houses the interquartile range (IQR), which is the middle 50% of the data; this includes the first quartile (Q1), the median, and the third quartile (Q3). The 'whiskers' extend from the box to the minimum and maximum values of the dataset.
03

Step 3. Understanding Summary Measures

The summary measures used in a box-and-whisker plot are minimum value, first quartile (Q1), median (which is the second quartile, Q2), third quartile (Q3), and maximum value. These five measures鈥揳lso known as the five-number summary鈥損rovide a comprehensive summary of the distribution of a dataset.

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Most popular questions from this chapter

The following data give the number of highway collisions with large wild animals, such as deer or moose, in one of the northeastern states during each week of a 9 -week period. \(\begin{array}{lllllllll}7 & 1 & 03 & 8 & 2 & 5 & 7 & 4 & 9\end{array}\) Find the range, variance, and standard deviation.

The mean time taken by all participants to run a road race was found to be 220 minutes with a standard deviation of 20 minutes. Using Chebyshev's theorem, find the percentage of runners who ran this road race in a. 180 to 260 minutes b. 160 to 280 minutes c. 170 to 270 minutes

Each year the faculty at Metro Business College chooses 10 members from the current graduating class that they feel are most likely to succeed. The data below give the current annual incomes (in thousands of dollars) of the 10 members of the class of 2000 who were voted most likely to succeed. \(\begin{array}{llllllllll}59 & 68 & 84 & 78 & 107 & 382 & 56 & 74 & 97 & 60\end{array}\) a. Calculate the mean and median. b. Does this data set contain any outlier(s)? If yes, drop the outlier(s) and recalculate the mean and median. Which of these measures changes by a greater amount when you drop the outlier(s)? c. Is the mean or the median a better summary measure for these data? Explain.

The following data set lists the number of women from each of 10 different countries who were on the Rolex Women's World Golf Rankings Top 25 list as of March 31,2009 . The data, entered in that order, are for the following countries: Australia, Brazil, England, Japan, Korea, Mexico, Norway, Sweden, Taiwan, and United States. \(\begin{array}{lllllllll}2 & 1 & 1 & 2 & 9 & 1 & 1 & 2 & 2 & 4\end{array}\) a. Calculate the mean and median for these data. b. Identify the outlier in this data set. Drop the outlier and recalculate the mean and median. Which of these two summary measures changes by a larger amount when you drop the outlier? c. Which is the better summary measure for these data, the mean or the median? Explain.

The mean time taken to learn the basics of a word processor by all students is 200 minutes with a standard deviation of 20 minutes. a. Using Chebyshev's theorem, find at least what percentage of students will learn the basics of this word processor in i. 160 to 240 minutes ii. 140 to 260 minutes \({ }^{*}\) b. Using Chebyshev's theorem, find the interval that contains the time taken by at least \(75 \%\) of all students to learn this word processor.
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