1. 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).

2. 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

3. Heat vs. Lakers 3/4/12
Minimum
Value
0
First
Quartile
3
Median
7
Third
Quartile
16
Maximum
Value
33

4. 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?

5. 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

6. 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?

7. 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”

8. 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.

9. 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.

10. Step Five: Draw Your Graph
X

11. Now you try!

12. #1
 What is the median of the set of data
below?
34, 22, 18, 32, 26, 56, 49, 40, 34, 41, 12
 34

13. #2
 What is the upper quartile of the set of
data below?
34, 22, 18, 32, 26, 56, 49, 40, 34, 41, 12
 41

14. #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

15. DROPS ON A PENNY!
partner activity
 You will need:
◦ Cup of water
◦ Penny
◦ Paper towel
◦ Eye dropper
◦ 4 sticky notes
◦ Pencil

16. 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!