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Descriptive Statistics: Stem and Leaf Graphs (Stemplots)

Module by: Susan Dean, Dr. Barbara Illowsky

Summary: This module introduces the use of stem-and-leaf graphs, or stemplots, for describing a set of data visually.

Note: You are viewing an old version of this document. The latest version is available here.

One simple graph, the stem-and-leaf graph or stemplot, comes from the field of exploratory data analysis.It is a good choice when the data sets are small. To create the plot, divide each observation of data into a stem and a leaf. The leaf consists of one digit. For example, 23 has stem 2 and leaf 3. Four hundred thirty-two (432) has stem 43 and leaf 2. Five thousand four hundred thirty-two (5,432) has stem 543 and leaf 2. The decimal 9.3 has stem 9 and leaf 3. Write the stems in a vertical line from smallest the largest. Draw a vertical line to the right of the stems. Then write the leaves in increasing order next to their corresponding stem.

Example 1

For Susan Dean's spring pre-calculus class, scores for the first exam were as follows (smallest to largest):

33; 42; 49; 49; 53; 55; 55; 61; 63; 67; 68; 68; 69; 69; 72; 73; 74; 78; 80; 83; 88; 88; 88; 90; 92; 94; 94; 94; 96; 100
Stem-and-Leaf Diagram
3 3
4 299
5 355
6 1378899
7 2348
8 03888
9 0244446
10 0

The stemplot shows that most scores fell in the 60s, 70s, 80s, and 90s. Eight out of the 31 scores or approximately 26% of the scores were in the 90's or 100, a fairly high number of As.

The stemplot is a quick way to graph and gives an exact picture of the data. You want to look for an overall pattern and any outliers. An outlier is an observation of data that does not fit the rest of the data. It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500) while others may indicate that something unusual is happening. It takes some background information to explain outliers. In the example above, there were no outliers.

Example 2

Create a stem plot using the data:

1.1; 1.5; 2.3; 2.5; 2.7; 3.2; 3.3; 3.3; 3.5; 3.8; 4.0; 4.2; 4.5; 4.5; 4.7; 4.8; 5.5; 5.6; 6.5; 6.7; 12.3

The data are the distance (in kilometers) from a home to the nearest supermarket.

Problem 1

  1. Are there any outliers?
  2. Do the data seem to have any concentration of values?

Hint:

The leaves are to the right of the decimal.

Solution 1

The value 12.3 may be an outlier. Values appear to concentrate at 3 and 4 miles.

Stem Leaf
1 1 5
2 3 5 7
3 3 3 3 5 8
4 0 2 5 5 7 8
5 5 6 6
6 5 7
7  
8  
9  
10  
11  
12 3

Note:

This book contains instructions for constructing a histogram and a box plot for the TI-83+ and TI-84 calculators. You can find additional instructions for using these calculators on the Texas Instruments (TI) website.

Glossary

Outlier:
An observation that does not fit the rest of the data.

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