Box & Whisker Plots
SDAP 1.3 (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).
Heat vs. Lakers 3/4/12
T. Murphy
0 points
S. Blake
3 points
A. Goudelock
7 points
A. Bynum
16 points
K. Bryant
33 points
Heat vs. Lakers 3/4/12
Minimum
Value
0
First
Quartile
3
Median
7
Third
Quartile
16
Maximum
Value
33
What is a box & whisker plot?
A box-and-whisker plot
◦ can be useful for handling many data values
◦ allow people to explore data and to draw
informal conclusions when two or more
variables are present
◦ show only certain statistics rather than all the
data
Think back on the Lakers… did the box-and-
whisker plot show rebounds? Fouls? Free throws?
Step One: Find the Median
(middle)
The following numbers are the amount of
marbles different boys own.
68 34 54 82 18 93 87 78 61 85 100 27 52 59 91
-------------------------------------------------------
To find the median, put the numbers in
order & find the one in the exact middle
18 27 34 52 54 59 61 68 78 82 85 87 91 93 100
Step Two: The Lower Quartile
Focus only on the values to the left of the
median: 18 27 34 52 54 59 61
Now we need to find the median of these
numbers
◦ Since they’re already in order it’s easy to see
the median of the values less than the median
is 52
This value is called the “Lower Quartile”
◦ Think ahead: Using your knowledge of prefixes
and suffixes, what does ‘quartile’ mean and
how will knowing this help us design our box-
and-whisker plot?
Step Three: The Lower Quartile
Now consider only the values to the right
of the median: 78 82 85 87 91 93 100
You should have noticed the median of
this set of numbers is 87
This value is called the “Upper Quartile”
Wait a minute… Too easy right?
What happens if you’re finding the median
in an ordered set with an even number of
values?
◦ You must first take the average of the two
middle numbers.
For example: 3, 5, 7, and 10.
Add the two middle numbers 5 + 7 = 12
Divide your answer by the
number of values added 12 / 2 = 6
6 is the average and your
median for this set.
Step Four: The Interquartile
Range
You’re now ready to find the Interquartile
Range (IQR).
The IQR is the difference between the
upper quartile and the lower quartile.
In our case the IQR = 87 – 52
IQR = 35
The IQR is a very useful measurement
because it is less influenced by extreme
values, it limits the range to the middle
50% of the values.
Step Five: Draw Your Graph
X
Now you try!
#1
What is the median of the set of data
below?
34, 22, 18, 32, 26, 56, 49, 40, 34, 41, 12
34
#2
What is the upper quartile of the set of
data below?
34, 22, 18, 32, 26, 56, 49, 40, 34, 41, 12
41
#3
What is the maximum value (upper
extreme) of the set of data below?
34, 22, 18, 32, 26, 56, 49, 40, 34, 41, 12
56
DROPS ON A PENNY!
partner activity
You will need:
◦ Cup of water
◦ Penny
◦ Paper towel
◦ Eye dropper
◦ 4 sticky notes
◦ Pencil
Directions
Working with a partner, take turns dropping
one drop of water at a time on the penny.
Both partners count the drops as you go to
assure for an accurate count.
When the water finally spills over the edge of
the penny record on your sticky note how
many drops you had before the water spilled
Each partner will take 2 turns
Be sure to dry the penny between turns
When your team is done, clean up and
construct a box-and-whisker plot for your
information.
◦ When everyone is finished we will make one for the
class’ results!
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