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Stem-and-leaf Graph or Stemplot

Date: 10/12/97 at 09:02:38
From: Scott Laurain
Subject: Stem leaf graph

Hi! I was doing a math-a-thon and I got a problem about a stem leaf 
graph. I am in the advanced math class. My math teacher said it would 
take two days to teach his advanced class how to do it. Can you help?

Date: 10/12/97 at 11:04:48
From: Doctor Chita
Subject: Re: Stem leaf graph

Hi Scott:

Sure, I can try to help.

A stem-and-leaf graph, also called a stemplot, is a way to represent 
the distribution of numeric data. It was invented by John Tukey, a 
mathematician, and is a quick way to picture data for numbers that are 
greater than 0. I'll explain using an example. 

Suppose you have the following set of numbers (they might represent 
the number of home runs hit by a major league baseball player during 
his career).

32, 33, 21, 45, 58, 20, 33, 44, 28, 15, 18, 25

The stem of a stemplot can have as many digits as needed, but the 
leaves should contain only one digit. To create a stemplot to display 
the above data, you must first create the stem. Since all of the 
numbers have just two digits, start by arranging the tens digits from 
smallest to largest. 

To create the leaves, draw a vertical bar after each of the tens 
digits and arrange the ones digits from each number in the data set in 
order from smallest to largest. If there are duplicate numbers, like 
33, list each one.


The shape of the resulting display looks something like a bar graph 
oriented vertically. By examining the stemplot, you can determine 
certain properties of the data.

You can find the median by counting from either end of the stemplot 
until you find its center. Here, since there are 12 numbers, the 
center lies between 28 and 32. The median is the average of the two 
data points: (28+32)/2 = 30.)

You can also determine if there is a mode in the data set by looking 
at the plot. Here, the number 33 is the mode since it is the only 
value that occurs more than once. 

If your data contain three digit numbers (like batting averages, for 
example), you can use the same technique. For example, let's assume 
the data are

298, 303, 285, 311, 225, 315, 250, 305 

Ignore the ones digits in each number (these will be the leaves) and 
look at the remaining two digits in each number (the hundreds and tens 
digits). The stem will begin at 22 because the smallest number in the 
data set is 225. The stem will end at 31 because the largest number is 
315. Include the two-digit numbers between 22 and 31 in the body of 
the stem. 

Once you have the stem, then list the ones digits in each number after 
the corresponding two-digit number before it. The stemplot will look 
like this, with no leaves after the numbers without a corresponding 


If these data represent the batting averages for a particular player, 
this display indicates that he has had a very successful career - most 
of his averages are clustered between 280 and 320. 

I hope this helps. 

-Doctor Chita,  The Math Forum
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Associated Topics:
High School Equations, Graphs, Translations

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