6th Grade Math Textbook, Fundamentals

 &KDSWHU

8-8

Key Concept

Box-and-Whisker Plot

upper quartile: median of the upper

half of the data

lower quartile: median of the lower

half of the data

upper extreme: greatest data value

lower extreme: least data value.

Box-and-Whisker Plots

Objective To read and make box-and-whisker plots •To determine and interpret clusters,

quartiles, gaps, and outliers of data • To compare two box-and-whisker plots using the same

number line

The table at the right shows how many minutes it took
each of 20 students to complete a math quiz. How could
this data be displayed in a box-and-whisker plot?

A is a graph that shows how the
data in a set are distributed, but it does notshow all the
values in the data set. It summarizes the spread of data
by dividing them into fourths along a number line. The median
of the data separates the data into halves. The are values
that divide the data into fourths. The median of the lower half
is the of the data, and the median of the upper half
is the of the data.

To make a box-and-whisker plot:

Draw a number line that includes the least and greatest data values.

Determine the median, the lower quartile, and the upper quartile of the data.

6.4, 6.5, 6.7, 6.8, 7. 1, 7. 3, 7.5, 7.6, 7.9, 8.2, 8.4, 8.8, 8.8, 8.9, 9.0, 9.4, 9.5, 10.1, 10.5, 10.5

upper quartile

lower quartile

quartiles

box-and-whisker plot

Length of Time in Minutes

8.8 7.5 9.5 8.4 9.4 6.4

10.1 6.7 8.2 10.5 7.6 7.3

10.5 9.0 6.5 7.9 8.9 8.8

6.8 7.1

Remember:The median for

an even set of numbers is

the mean of the two middle

numbers when the set is

listed in order from least to

greatest or from greatest

to least.

Locate these three points on the number line, and draw

the box. The box extends from the lower quartile to the

upper quartile. Draw a vertical line segment in the box

through the median. The length of the box along the

number line represents the spread of the middle half

of the data.

Draw the lines (“whiskers”) on the box from the upper

quartile to the greatest value, called the ,

and from the lower quartile to the least value, called the

lower extreme.

upper extreme

67891011

1

4

1

4

1

4

1

4

lower

extreme

lower

quartile median

upper

quartile upper

extreme

Each part is one fourth of the data,

even though the visual may not show

four parts of equal size.

Median of Lower Half:

7.2

7.2 Lower Quartile

7.1 7. 3

2

Median:

8.2  2 8.48.3

Median of Upper Half:

9.2

9.2 Upper Quartile

9.0 9.4

2