Creating and Interpreting Stemplots

1
Creating and Interpreting Stemplots
2
Creating and Interpreting Stemplots

• In this presentation, you will learn about both
  basic stemplots as well as different advanced
  stemplots.

3
Basic Stemplots

• A stemplot is quite similar to a dotplot.
• Like the dotplot, the stemplot is arranged along
  a type of number line (stems).
• Instead of plotting dots above corresponding
  points, you place (in order) leaves above the
  points.
• Lets consider how it looks in an example.

4
Basic Stemplots

• Consider the dataset comprised of peoples ages
  at a family reunion.
• Their ages are
• 4, 6, 7, 13, 16, 17, 23, 31, 36, 40, 42, 44,
  53, 57, 58, 62, 84

5
Basic Stemplots

• A dotplot would be cumbersome and too spread out
  to be informative (consider numbering off the
  number line from 4 to 84).
• A stemplot will group the data together, thus
  compacting the graph and making it easier to
  visualize the data.

6
Basic Stemplots

• To create the stemplot, first determine the
  stems.
• The stems in this case should be the tens place
  (the values in the tens place range from 0 to 8.
• Create your number line from 0 to 8.
• This is typically done vertically.

7
Basic Stemplots

• Then, place the leaves next to the corresponding
  stems in sequential order.
• Each digit placed as a stem should take up the
  same amount of space to provide a visual sense of
  how many values fall in that area of the number
  line.

8
Basic Stemplots

• Things to note include describing the center,
  shape, spread, and extreme values (outliers) of
  the distribution.
• The center seems to be around the low 40s.
• The shape is a bit odd certainly not bell-shaped
  as it seems to have two peaks. This is typically
  referred to as bimodal.
• The spread is what you might expect for data
  representing ages of humans.
• It seems like the 84 year-old may be an outlier.

9
Basic Stemplots

• Imagine turning the stemplot on its side (by
  rotating it counter-clockwise 90 degrees).
• It would then resemble our bar charts of before.
• A key difference though, is that the graph depict
  quantitative data rather than qualitative.
• This distinction makes the rotated stemplot a
  much closer relative to the bar chart.

10
Basic Stemplots

• This can be further transformed into the
  following (which is really a histogram).

11
Basic Stemplots

• Some helpful conveniences of stemplots
• They are relatively easy to construct (especially
  when you are without technology)
• They still display each data point (meaning you
  can do some calculations with what is presented
  in the display)
• Imagine the actual histogram with the bars, but
  with the numbers in the bars eliminated.
• Would it be possible (without those numbers) to
  calculate the actual mean or median?

12
Advanced Stemplots

• Many times, the data does not lend itself to tens
  digits and units digits (in fact, it rarely
  does).
• In most cases you will need to do some rounding
  or truncating (cutting off the excess digits for
  the purpose of the graph) of the figures (see
  example 1).
• Also, you may need split the stems.
• This means you may have two stems for each
  leading digit. The first stem will contain
  leaves from 0 to 4 and the second stem will
  contain leaves from 5 to 9.
• See the example 2 below for clarification.
• Finally you may want to construct back-to-back
  stemplots in order to compare two distribution.
• See example 3.

13
Example 1 - Rounding

• Original Data
• 2.234, 3.23525, 3.76447, 3.794, 4.252, 4.8886
• Revised Data (after rounding)
• 2.2, 3.2, 3.8, 3.8, 4.3, 4.9
• Stemplot (done in StatCrunch plus it rounds for
  you!)
• 2 2
• 3 288
• 4 39

14
Example 2 Split Stems

• Original Data
• 1.1, 1.2, 1.4, 1.6, 1.6, 1.7, 1.9, 1.9, 2.0, 2.0,
  2.3, 2.5, 2.7, 3.5
• Unfortunately, StatCrunch will not split stems.
• 1 12466799 1 124
• 2 00357 OR 1 66799
• 3 5 2 003
• 2 57
• 3
• 3 0
• Which of the above plots is more telling with
  regards to the shape, center, spread, and
  extremes of the distribution?

15
Example 3 Back-to-Back Stemplots

• Original data consists of two datasets. Consider
  the number of home runs hit by Barry Bonds and
  Mark McGwire from the years 1987 to 2001.

• To construct the back-to-back stemplot, the stems
  go down the middle.
• On the left-hand side, plot one of your
  distributions data points (see McGwires data on
  the left).
• Notice the ordering of the leaves on McGwires
  side of the stemplot.
• On the right-hand side, plot your regular
  stemplot.
• This plot is useful in comparing distributions.
  It can quickly give the educatied reader a sense
  of how the center, shape, extremes and spread of
  two distributions compare.

16
Creating and Interpreting Stemplots

• This concludes the presentation.