California
Standards
SDAP1.1 Know various forms of display
for data sets, including a stem-and-leaf plot or
box-and-whisker plot; use the forms to display
a single set of data or to compare two sets of
data.
SDAP1.3 Understand the meaning
of, and be able to compute, the minimum, the
lower quartile, the median, the upper quartile,
and the maximum of a data set.
Objective:
Today we will display and
analyze data in box-and-whisker
plots.
APK
Teacher I do
1. Order the test scores from least to
greatest: 89, 93, 79, 87, 91, 88, 92.
79, 87, 88, 89, 91, 92, 93
2. Find the median of the test scores.
89
Students complete:
Find the median of the following test scores?
65, 75, 92, 90, 74, 86, 98
We will need to know how to find the median in order
to make box and whisker plots.
Vocabulary
lower quartile
upper quartile
box-and-whisker plot
minimum
maximum
A box-and-whisker plot shows the distribution of data.
The middle half of the data is represented by a “box” with
a vertical line at the median.
The box extends to the upper and lower quartiles.
The upper quartile is the median of the upper half of
the data. The lower quartile is the median of the lower
half of the data.
Data set: 85,92,78,88,90,88,89
78
85
Lower quartile
88
88
Median
89
90 92
Upper quartile
What is a box-and-whisker plot?
What are the upper and lower quartiles?
The lower fourth and upper fourth quarters are
represented by “whiskers” that extend to the minimum
(least) and maximum (greatest) values.
Data set: 85,92,78,88,90,88,89
78
Lower quartile
85
88
88
Median
89
90 92
Upper quartile
What are minimum and maximum values?
The table below summarizes a cat breeder’s
records for kitten litters born in a given year. You
can divide the data into four equal part using
quartiles.
Litter Size
2
3
4
5
6
Number of
Litters
1
6
8
11
1
You know that the median of a data set divides the
data into a lower half and an upper half. The median
of the lower half is the lower quartile, and the
median of the upper half is the upper quartile.
Kitten Data
Lower half
Upper half
233333344444444555555555556
Upper quartile: 5
Lower quartile: 3
median of upper half
median of lower half
Median: 4
You know that the median of a data set divides the
data into a lower half and an upper half. The median
of the lower half is the lower quartile, and the
median of the upper half is the upper quartile.
Kitten Data
Lower half
Upper half
233333344444444555555555556
Upper quartile: 5
Lower quartile: 3
median of upper half
median of lower half
Median: 4
What letter is the _____?
F
E
D
Lower half
Upper half
233333344444444555555555556
B
A
How do you know?
c
Importance
Why do we need to know how to display and analyze
data in box-and-whisker plots ?
*It helps you to interpret and represent data.
*It gives a visual representation of data.
Tell your partner which reason is most important to
you. You can use one of mine or one of your own.
p/s - volunteers
Find the lower and upper quartiles for the data
set.
1. Order the data from least to greatest.
2. Find the median.
3. Find the median of the lower half – lower quartile
4. Find the median of the upper half – upper quartile
I do
A. 15, 83, 75, 12, 19, 74, 21
12 15 19 21 74 75 83
Order the values.
lower quartile: 15
upper quartile: 75
How did I find the lower and upper quartiles?
Find the lower and upper quartiles for the data
set.
1. Order the data from least to greatest.
2. Find the median.
3. Find the median of the lower half – lower quartile
4. Find the median of the upper half – upper quartile
We do
B. 75, 61, 88, 79, 79, 99, 63, 77
61 63 75 77 79 79 88 99
lower quartile:
Order the values.
63 + 75
= 69
2
79 + 88
upper quartile:
= 83.5
2
Find the lower and upper quartiles for the data
set.
1. Order the data from least to greatest.
2. Find the median.
3. Find the median of the lower half – lower quartile
4. Find the median of the upper half – upper quartile
We do
A. 25, 38, 66, 19, 91, 47, 13
13 19 25 38 47 66 91
lower quartile: 19
upper quartile: 66
Order the values.
Find the lower and upper quartiles for the data
set.
1. Order the data from least to greatest.
2. Find the median.
3. Find the median of the lower half – lower quartile
4. Find the median of the upper half – upper quartile
You do
B. 45, 31, 59, 49, 49, 69, 33, 47
31 33 45 47 49 49 59 69
Order the values.
33 + 45
lower quartile:
= 39
2
49 + 59
upper quartile:
= 54
2
I do:
Additional Example 2: Making a Box-and-Whisker Plot
Use the given data to make a box-and-whisker plot.
21, 25, 15, 13, 17, 19, 19, 21
Step 1. Order the data from least to greatest. Then
find the minimum, lower quartile, median, upper
quartile, and maximum.
13 15 17 19 19 21 21 25
minimum: 13
15 + 17
lower quartile:
2
maximum: 25
= 16 upper quartile:
median:
19 + 19
2
= 19
21 + 21
2
= 21
I do (cont.)
Additional Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 2. Draw a number line and plot a point above
each value from Step 1.
13 15 17 19 19 21 21 25
12
14
16
18
20
22
24
26 28
I do (cont.)
Additional Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 3. Draw the box and whiskers.
13 15 17 19 19 21 21 25
12
14
16
18
20
22
24
26 28
We do
Check It Out! Example 2
Use the given data to make a box-and-whisker plot.
31, 23, 33, 35, 26, 24, 31, 29
Step 1. Order the data from least to greatest. Then
find the minimum, lower quartile, median, upper
quartile, and maximum.
23 24 26 29 31 31 33 35
minimum: 23
lower quartile:
maximum: 35
24 + 26
2
= 25 upper quartile:
median: 29 + 31 = 30
2
31 + 33
2
= 32
We do (cont.)
Check It Out! Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 2. Draw a number line and plot a point above
each value.
23 24 26 29 31 31 33 35
22
24
26
28
30
32
34
36 38
We do (cont.)
Check It Out! Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 2.
3. Draw a
the
box and
whiskers.
number
line
and plot a point above
each value.
23 24 26 29 31 31 33 35
22
24
26
28
30
32
34
36 38
Step 1. Order the data from least to greatest. Then find
the minimum, lower quartile, median, upper quartile, and
maximum.
Step 2. Draw a number line and plot a point above each
value.
Step 3. Draw the box and whiskers.
Additional Guided Practice:
With partners:
Page 544 #1
You do:
Page 544 #2
Closure
What uses upper and lower quartiles, the median, the
maximum, and the minimum to show a set of data?
Find the lower and upper quartiles for each
data set.
1. 48, 52, 68, 32, 53, 47, 51
lower = 47; upper = 53
Closure (cont.)
Use the following data for problems 3 and 4.
91, 87, 98, 93, 89, 78, 94
3. Make a box-and-whisker plot.
78
87
91
94
98
What did you learn today about box-and-whisker plots?