Unit 2 Lesson 2(3.2)

Graphical Methods for Describing Data3.2: Stem-and-Leaf Plots

Stem-and-Leaf DisplaysWhen to Use Univariate numerical data

How to construct– Select one or more of the leading digits for the stem– List the possible stem values in a vertical column– Record the leaf for each observation beside each

corresponding stem value– Indicate the units for stems and leaves in a key or

legend

To describe – comment on the center, spread, and shape of the

distribution and if there are any unusual features

Each number is split into two parts:

Stem – consists of the first digit(s)Leaf - consists of the final digit(s)

Use for small to moderate sized

data sets. Doesn’t work well for large data sets.

Be sure to list every stem

from the smallest to the largest value

If you have a long lists of leaves behind a few

stems, you can split stems in order to

spread out the distribution.

Can also create comparative stem-and-leaf displays

The following data are price per ounce for various brands of different brands of dandruff shampoo at a local grocery store.

0.32 0.21 0.29 0.54 0.17 0.28 0.36 0.23

Create a stem-and-leaf display with this data? Stem Leaf

.1

.2

.3

.4

.5

What would an appropriate stem be?

List the stems vertically

For the observation of “0.32”, write the 2 behind the “3” stem.

2

Continue recording each leaf with the

corresponding stem 1 9

4

7

8

6

3

The Census Bureau projects the median age in 2030 for the 50 states and Washington D.C. A stem-and-leaf display is shown below.

Notice that you really cannot see a distinctive

shape for this distribution due to the long list of

leaves

We can split the stems in order to better see the

shape of the distribution.

Notice that now you can see the

shape of this distribution.

We use L for lower leaf values (0-4) and H for higher leaf values (5-

9).

The following is data on the percentage of primary-school-aged children who are enrolled in school for 19 countries in Northern Africa and for 23 countries in Central African.

Northern Africa54.6 34.3 48.9 77.8 59.6 88.5 97.4 92.5 83.9 98.891.6 97.8 96.1 92.2 94.9 98.6 86.6 96.9 88.9

Central Africa58.3 34.6 35.5 45.4 38.6 63.8 53.9 61.9 69.9 43.085.0 63.4 58.4 61.9 40.9 73.9 34.8 74.4 97.461.0 66.7 79.6

Create a comparative stem-and-leaf display. What is an appropriate

stem?

Let’s truncate the leaves to the unit place.

“4.6” becomes “4”

How Many Pairs of Shoes Do You Own?

Homework

• Pg.62: #3.15, 3.17, 3.19, 3.20