The five-number summary can be used to describe the spread of a data set.

One graphical display, a box-and-whiskers plot, is very useful for visualizing these numbers and showing the spread of data over a number line. In this section, you will learn how to construct and interpret a box-and-whiskers plot.

The table below shows the population of 10 large cities in the United States, according to the U.S. Census Bureau, in 2011.

 10 Large Cities in the United States Rank City Population 11 Jacksonville, FL 827,908 12 Indianapolis, IN 827,609 13 Austin, TX 820,611 14 San Francisco, CA 812,826 15 Columbus, OH 797,434 16 Fort Worth, TX 758,738 17 Charlotte, NC 751,087 18 Detroit, MI 706,585 19 El Paso, TX 665,568 20 Memphis, TN 652,050

For this data set, calculate the minimum, lower quartile, median, upper quartile, and maximum values.

Interactive popup. Assistance may be required.

The numbers are already in order from greatest to least. The median is the average of the middle two numbers, the minimum and maximum are the extreme values, the lower quartile is the median of the lower half of the data, and the upper quartile is the median of the upper half of the data. Interactive popup. Assistance may be required.

Minimum: 652,050
Lower Quartile: 706,585
Median: 778,086
Upper Quartile: 820,611
Maximum: 827,908

Each of the tiles in the interactive represents one of the numbers in the five-number summary for this data set. Drag each tile to its appropriate place on the number line. When all five tiles are placed correctly, "Well Done" will appear.

Next, click the Construct Box button to construct the box portion of the box-and-whiskers plot.

Next, click the Construct Whiskers button to construct the whiskers portion of the box-and-whiskers plot.

A box-and-whiskers plot is useful because it tells you at a glance where each quartile of the data set lies on a number line. A box-and-whiskers plot gives you a sense of the spread of the data.

### Practice

1. The revenue, in billions of dollars, for the 10 largest U.S. businesses in 2008 is shown in the table.
2.  10 Largest Businesses in U.S., 2008 Business Revenue (billions of dollars) Wal-Mart 378.8 ExxonMobil 372.8 Chevron 210.8 General Motors 182.3 ConocoPhillips 178.6 General Electric 176.7 Ford Motor 172.5 Citigroup 159.3 Bank of America Corp. 119.2 AT&T 118.9 Source: www.infoplease.com

Which box-and-whiskers plot best matches the data shown in the table?

Interactive popup. Assistance may be required.

The endpoints of the whiskers represent the minimum and maximum values of the data set. Interactive popup. Assistance may be required.

Graph B
3. The box-and-whiskers plot below shows the number of gold medals earned in the summer Olympics by the 10 countries with the most gold medals from 1896 to 2008.

The chart below shows statements related to the graph. Decide if each statement is supported by the information in the graph, and click the appropriate box next to the statement.