1. Analyzing One-Variable Data
Lesson 1.4
Displaying Quantitative Data: Stemplots
Statistics and Probability with Applications, 3rd Edition
Starnes, Tabor
Bedford Freeman Worth Publishers

2. Displaying Quantitative Data: Stemplots
Learning Targets
After this lesson, you should be able to:
Make stemplots of quantitative data.
Interpret stemplots.
Compare distributions of quantitative data with stemplots.

3. Displaying Quantitative Data: Stemplots
Another simple type of graph for displaying quantitative data is a stemplot (also called a stem-and-leaf plot).
Stemplot
A stemplot shows each data value separated into two parts:
a stem, which consists of all but the final digit, and
a leaf, the final digit.
The stems are ordered from lowest to highest and arranged in a vertical column. The leaves are arranged in increasing order out from the appropriate stems.
Caffeine Content of Various Soft Drinks

4. Displaying Quantitative Data: Stemplots
How to Make a Stemplot
Make stems. Separate each observation into a stem, consisting of all but the final digit, and a leaf, the final digit. Write the stems in a vertical column with the smallest at the top. Draw a vertical line at the right of this column. Do not skip any stems, even if there is no data value for a particular stem.
Add leaves. Write each leaf in the row to the right of its stem.
Order leaves. Arrange the leaves in increasing order out from the stem.
Add a key. Provide a key that explains in context what the stems and leaves represent.

5. Displaying Quantitative Data: Stemplots
We can get a better picture of the data by splitting stems.
In graph (a), the values from 0 to 9 are placed on the “0” stem.
Graph (b) shows another stemplot of the same data. This time, values having leaves 0 through 4 are placed on one stem, while values ending in 5 through 9 are placed on another stem. This is called splitting the stems. Use this strategy if there is a cluster of data in any one stem.
Now we can see the shape of the distribution more clearly.

6. Displaying Quantitative Data: Stemplots
Tips to Consider Before Making a Stemplot
There is no magic number of stems to use. Too few or too many stems will make it difficult to see the distribution’s shape.
Five stems is a good minimum.
If you split stems, be sure that each stem is assigned an equal number of possible leaf digits.
When the data have too many digits, you can get more flexibility by rounding or truncating the data.

7. Displaying Quantitative Data: Stemplots
You can use a back-to-back stemplot with common stems to compare the distribution of a quantitative variable in two groups. The leaves on each side are placed in order on each side of the common stem.
How many pairs of shoes does a typical teenager own?

8. How many shoes are too many shoes?
LESSON APP 1.4
How many shoes are too many shoes?
How many pairs of shoes does a typical teenager own? To find out, a group of statistics students surveyed separate random samples of 20 female students and 20 male students from their large high school. Then they recorded the number of pairs of shoes that each person owned. Here are the data.
Females 50 26 31 57 19 24 22 23 38 13 34 30 49 15 51
Males 14 7 6 5 12 8 10 11 4 35
Make a stemplot of the female data. Do not split stems.
Describe the shape of the distribution.
Explain why we should split stems for the male data.
The back-to-back stemplot with split stems displays the data for both genders. Write a few sentences comparing the male and female distributions.

9. Displaying Quantitative Data: Stemplots
Learning Targets
After this lesson, you should be able to:
Make stemplots of quantitative data.
Interpret stemplots.
Compare distributions of quantitative data with stemplots.