 # 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 58 would be split as:

```        Stem  |  Leaf
5  |  8
```

### Here is a typical Example: ```Message from your Math instructor.
Results of Exam1 are presented
with a stem-and-leaf graph.

Class Scores:
75,8,36,36,55,55,27,83,17,58,
55,42,36,50,42,82,27,92,50,42,
100,83,27,58,55

Your score out of 100 is at the end of this message.

All the grades are listed.
The scores go from 8 to 100.

The Stem-and-leaf is:

N = 25   Median = 50
Quartiles = 36, 58

Decimal point is 1 place to the right of the colon

0 : 8
1 : 7
2 : 777
3 : 666
4 : 222
5 : 00555588
6 :
7 : 5
8 : 233
9 : 2
10 : 0

--------------------------------------------------
STUDENT NAME             USERID  EX1
Brown Charlie            CB1234  55
``` ### Constructing a stem-and-leaf plot:

Consider again the scores in Exam1 for the class of 25 students above:
```75,8,36,36,55,55,27,83,17,58,
55,42,36,50,42,82,27,92,50,42,
100,83,27,58,55
```
Writing the data in numerical order may help to organize the data, but is NOT a required step. Ordering can be done later.

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.

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.

A stem-and-leaf plot shows the shape and distribution of data. It can be clearly seen in the example below that the data is distributed around the row with a stem of 5. There is a clear subgroup of "good students" with scores from 75 to 100.

#### 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.

Carlos Rodriguez <carlos@math.albany.edu>