Math A

Stem-and-Leaf Plots

Data can be displayed in many ways.  One method of displaying a set of data is with a stem-and-leaf plot.

  A stem-and-leaf plot is a display that organizes data to show its shape and distribution.

In a stem-and-leaf plot each data value is split into a "stem" and a "leaf".  The "leaf" is usually the last digit of the number and the other digits to the left of the "leaf" form the "stem".  The number 123 would be split as:

stem  12
leaf 3

  

Constructing a stem-and-leaf plot:

The data: Math test scores out of 50 points:  35, 36, 38, 40, 42, 42, 44, 45, 45, 47, 48, 49, 50, 50, 50.

Writing the data in numerical order may help to organize the data, but is NOT a required step.  Ordering can be done later.

35, 36, 38, 40, 42, 42, 44, 45, 45, 47, 48, 49, 50, 50, 50

Separate each number into a stem and a leaf.  Since these are two digit numbers, the tens digit is the stem and the units digit is the leaf.  

The number 38 would be represented as

 Stem Leaf
3 8

Group the numbers with the same stems.  List the stems in numerical order.  (If your leaf values are not in increasing order, order them now.)  Title the graph.

Math Test Scores
 (out of 50 pts)
Stem Leaf
3

5 6 8 

4

0 2 2 4 5 5  7 8 9 

5

0 0 0 

Prepare an appropriate legend
(key) for the graph.

Legend:  3 | 6  means 36

A stem-and-leaf plot shows the shape and distribution of data.  It can be clearly seen in the diagram above that the data clusters around the row with a stem of 4.

Notes:

  • The leaf is the digit in the place farthest to the right in the number, and the stem is the digit, or digits, in the number that remain when the leaf is dropped.

  • To show a one-digit number (such as 9) using a stem-and-leaf plot, use a stem of 0 and a leaf of 9.

  • To find the median in a stem-and-leaf plot, count off half the total number of leaves.

Special Case:

If you are comparing two sets of data, you can use a back-to-back stem-and-leaf plot.

Data Set A   Data Set B
Leaf Stem Leaf

3 2 0

4 1 5 6 7

The numbers 40, 42, and 43 are from Data Set A.
The numbers 41, 45, 46, and 47 are from Data Set B.

 

Are Stem-and-Leaf Plots "tipped over" Histograms?
A stem-and-leaf plot does resemble a histogram turned sideways.  The stem values could represent the intervals of a histogram, and the leaf values could represent the frequency for each interval.

One advantage to the stem-and-leaf plot over the histogram is that the stem-and-leaf plot displays not only the frequency for each interval, but also displays all of the individual values within that interval.

 

Greyblue.jpg (6110 bytes)

 

 


Roberts

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