7th Grade Math

Lesson 2B Measures of Variation 505

Construct a Box-

and-Whisker Plot

DRIVING The list below shows the speeds of eleven cars. Draw a

box-and-whisker plot of the data.

25 35 27 22 34 40 20 19 23 25 30

Step 1 Order the numbers from least to greatest. Then draw a

number line that covers the range of the data.

10 15 20 25 30 35 40 45 50

Step 2 Find the median, the extremes, and the upper and lower

quartiles. Mark these points above the number line.

LQ: 22 median: 25 UQ: 34

lower

extreme: 19

10 15 20 25 30 35 40 45 50

upper

extreme: 40

Step 3 Draw the box so that it includes the quartile values. Draw

a vertical line through the box at the median value. Extend

the whiskers from each quartile to the extreme data points.

10 15 20 25 30 35 40 45 50

a. Draw a box-and-whisker plot of the data set below.

{$20, $25, $22, $30, $15, $18, $20, $17, $30, $27, $15}

Interpret Data

DRIVING Refer to the box-and-whisker plot in Example 1.

Half of the drivers were driving faster than what speed?

Half of the drivers were driving faster than 25 miles per hour.

What does the box-and-whisker plot’s length tell about the data?

The length of the left half of the box-and-whisker plot is short. This

means that the speeds of the slowest half of the cars are concentrated.

The speeds of the fastest half of the cars are spread out.

b. What percent were driving faster than 34 miles per hour?

Common Misconception Common Misconception

You may think that the

median always divides

the box in half. However,

the median may not

divide the box in half

because the data may

be clustered toward one

quartile.

Box-and-Whisker Plots Box-and-Whisker Plots

• If the length of a whisker
  or the box is short, the
  values of the data in that
  part are concentrated.


• If the length of a whisker
  or the box is long, the
  values of the data in that
  part are spread out.

498_509_C09_L2_895130.indd 505 1/11/10 9:34 AM