Unit 2 : Data Analysis
Box Plots
CCSS: S.ID.1, S.ID.2, S.ID.3
Graphical Representations Recap
• So far: Graphs are good because...
• Dot plots are a good graphical representation
of a distribution if ...
• Other good graphical representations include
box plots and histograms
• Let’s discuss box plots now (histograms will be
later)
Box plots look like...
What are the different parts that
make up a box plot?
• Minimum:
• 1st Quartile:
• Median:
• 3rd Quartile:
• Maximum:
Five-Number Summary
• We use minimum, 1st quartile, median, 3rd
quartile, and maximum to create box plots
• Five numbers... We call this the five-number
summary
• Five number summary is always used to
create box plots. Always.
Why do we use the median in box
plots?
• A median is a type of average
• There are other types of averages, like a mean
or a mode
• What’s the difference between median, mean,
mode?
• Why do we use the median (and not the mean
or mode) in box plots?
Let’s look at a simple distribution ...
• To help us understand why we need to use the
median in box plots
• Cost of five randomly selected jeans were $27,
$27, $29, $35, $450
• What’s the mode?
• What’s the mean?
• What’s the median?
So we use the median when
creating box plots because...
• Discuss in your groups for one minute
We use the median in box plots
because...
• The median is resistant (median is not
influenced by extreme values)
• The median doesn’t change even if there is a
value in the distribution that is very far away
from all the other values
• The median helps create a box plot that is not
misleading
Let’s create a box plot. We asked a random sample of
21 juniors at Canyon how many songs they have on
their iPods/mp3s.
233
25
160
12
242
79
261
93
251
155
49
145
193
191
266
260
173
168
184
145
259
Organize Data:
1) Arrange data smallest to greatest
2) Count in and find middle value (median)
3) Count in and find 1st quartile
4) Count in and find 3rd quartile
5) Identify min and max
Create box plot: Remember to put horizontal scale on bottom,
labeled; label with values of each of the 5-number summary
values; use context labels to clearly state what the box plot
represents
SOCS (Shape, Outlier(s), Center,
Spread)
• Let’s analyze the data using SOCS
Student Heights from Last Class
• Use the heights you put on the board last class
to create a box plot.
• Compare and contrast the dot plot and box
plot (different graphical representations of the
same data). Which is ‘better’??
What do you think are pros and cons
of using a box plot?
Did you think of these possible
advantages and disadvantages?
• Pros/Advantages:
– we see overall shape and trends well in box plot
– we keep original data when doing a dot plot
• Cons/Disadvantages:
– we lose the original values when creating a box plot
– sometimes more difficult to see trends and overall
shape of data in dot plot if data is spread out a lot