Box-and-Whisker
Plots
Making and Interpreting
Box-and-Whisker Plots
Becky Afghani
LBUSD Math Office
2003
You will:
Construct and
Interpret
Box and Whisker Plots
What is a Box-and Whisker
Plot?
• Suppose you have a large set of data
and want to know how it is
distributed.
• Think of a teacher’s class set of test
scores.
• A box-and-whisker plot displays the
median, the quartiles, and the
greatest and least values.
Why use a Box-and Whisker
Plot?
• The box-and-whisker plot is a visual
way to show the data.
• The median and quartiles can easily
be read.
• The shape of the box and the
whiskers gives information about how
the numbers are spread out.
Who uses Box-and Whisker
Plots?
• Scientists who perform experiments
display their results using box-andwhisker plots.
• Medical researchers display their
findings using box-and-whisker plots.
• Anyone who reads a scientific report
needs to understand how a box-andwhisker works.
We will make a Box-and
Whisker Plot
Here are all of the test scores from
your class on the last math test. (Not
really!)
87
75
83
94
100
74
68
98
99
85
83
100
72
68
100
You will need a five-number
summary in order to
construct the box-andwhisker plot.
Minimum
Lower quartile (Q1)
Median (Q2)
Upper quartile (Q3)
Maximum
?
?
?
?
?
Step 1: Write the data in
order from least to greatest.
87
75
83
94
100
74
68
98
99
85
83
100
72
68
100
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100
Step 2: Find the minimum and
maximum values of the data.
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100
minimum
maximum
The minimum is 68.
The maximum is 100.
Tell your neighbor how to
find the minimum and
maximum.
To find the
minimum...
To find the
maximum...
Step 3: Find the median of the
data.
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100
7 in the lower half
7 in the upper half
1 in the middle
The median is 85.
Tell your neighbor how to
find the median.
To find the
median...
Step 4: Find the lower quartile
(Q1) of the data.
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100
lower half
upper half
The middle number is
not in the lower or
upper half.
Step 4: Find the lower quartile
(Q1) of the data.
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100
lower half
upper half
The lower quartile is 74.
Choral Response: What is
the lower quartile?
The median of
The
median
of
the
lower
half
The median of
the lower half
the lower half
The median of
the lower half
The median of
the lower half
Step 5: Find the upper quartile
(Q3) of the data.
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100
lower half
upper half
The middle number is
not in the upper or
upper half.
Step 5: Find the upper quartile
(Q3) of the data.
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100
lower half
upper half
The upper quartile is 99.
Choral Response: What is
the upper quartile?
The median of
The
median
of
the
upper
half
The median of
the upper half
the upper half
The median of
the upper half
The median of
the upper half
Now that we have our fivenumber summary, we can
construct the box-andwhisker plot.
Minimum
Lower quartile (Q1)
Median (Q2)
Upper quartile (Q3)
Maximum
68
74
85
99
100
Write in Your Notes:
What are the five items in
the five number summary?
I can think
of one...
I bet
he knows!
Step 6: Draw a number line
that can show the data.
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100
50
60
70
80
90
100
Step 7: Mark the minimum,
maximum, median and both
quartiles on the number line.
Minimum
Lower quartile (Q1)
Median (Q2)
Upper quartile (Q3)
Maximum
50
60
70
80
68
74
85
99
100
90
100
Step 8: Draw a box between
the lower and upper quartiles.
Minimum
Lower quartile (Q1)
Median (Q2)
Upper quartile (Q3)
Maximum
50
60
68
74
85
99
100
70
80
90
100
Step 9: Draw a vertical line
through the median.
Minimum
Lower quartile (Q1)
Median (Q2)
Upper quartile (Q3)
Maximum
50
60
68
74
85
99
100
70
80
90
100
Step 10: Draw two “whiskers”
from the quartiles to the
minimum and maximum.
Minimum
Lower quartile (Q1)
Median (Q2)
Upper quartile (Q3)
Maximum
50
60
68
74
85
99
100
70
80
90
100
Interpreting the box-andwhisker plot
25%
50
60
70
25%
80
25%
90
Remember these are test scores.
25% of the test scores are in each
whisker and each section of the box.
25%
100
Find the false statement.
74
68
50
60
70
85
80
90
A) One fourth of the test scores were
between 85 and 99.
B) One half of the test scores were
between 74 and 99.
C) One half of the test scores were
between 85 and 100.
D) Three fourths of the test scores
were between 68 and 85.
99
100
100
Make another box-andwhisker plot from this data:
Age at First Inauguration of
American Presidents from 1900 to 1999
4
5
6
2 3 6
1 1 1 2 4 4 5 5 6 6
0 1 2 4 9
42 is 42 years
Minimum and Maximum
Age at First Inauguration of
American Presidents from 1900 to 1999
4
5
6
2 3 6 42 is the minimum
1 1 1 2 4 4 5 5 6 6
0 1 2 4 9
42 is 42 years
69 is the maximum
What is
many
Median How
halfway
What
is
data items
between
Age at First Inauguration
ofof 18?
half
are there?
American Presidents from 1900
to 1999
54 and
55?
4
5
6
2 3 6
1 1 1 2 4 4 ?5 5 6 6
0 1 2 4 9
42 is 42 years
18 items
54.5 is the
9
10
median
item
item
th
th
How many
Lower Quartile
items
Whichare
item
9isitems
in
the
in
lower
th
the
The
5
item
Age at First Inauguration of
half?
middle?
American Presidents from 1900
to 1999
4
5
6
2 3 6
1 1 1 2 4 4 5 5 6 6
0 1 2 4 9
54.5
42 is 42 years
51 is the
lower quartile
How many
Upper Quartile
items
Whichare
item
9isitems
in
the
in
upper
th
the
The
5
item
Age at First Inauguration of
half?
middle?
American Presidents from 1900
to 1999
4
5
6
2 3 6
1 1 1 2 4 4 5 5 6 6
0 1 2 4 9
54.5
42 is 42 years
60 is the
upper quartile
The Box-and-Whisker Plot
Age at First Inauguration of
American Presidents from 1900 to 1999
4
5
6
54.5
2 3 6
1 1 1 2 4 4 5 5 6 6
0 1 2 4 9
42 is 42 years
40
50
60
70
Find the false statement.
40
50
60
A) The oldest president at his
inauguration was 69.
B) One fourth of the presidents were
60 or over when inaugurated.
C) One half of the presidents were
inaugurated between ages 50 and 60.
D) The youngest president to be
inaugurated in the 1900s was 42.
70
Multiple Box-and-Whisker
Plots Can Be Used to
Compare Data
Average Monthly High Temperatures in Anchorage, Alaska
0
10
20
30
40
50
60
70
80
90
100
Average Monthly High Temperatures in Long Beach, California
0
10
20
30
40
50
60
70
80
90
100
Find the false statement.
Average Monthly High Temperatures in Anchorage, Alaska
0
10
20
30
40
50
60
70
80
90
100
0
10
20
30
40
50
60
70
80
90
100
Average Monthly High Temperatures in Long Beach, California
A) The range of average monthly high
temperatures is broader in Anchorage
than in Long Beach.
B) The average monthly high temperatures in
Long Beach are warmer than Anchorage.
C) Half of the average monthly highs in Long
Beach are between 27 and 59 degrees.
In your notes...
1. List the five items required
for a box-and-whisker plot.
2. Write a short description
for each.