## Stem and Leaf Diagrams

The stem and leaf graph allows easy recording and display of data in order. From a stem and leaf graph measures such as the median and quartiles can easily be found.

### Stem and Leaf Diagram

A stem and leaf diagram or chart provides a means of ordering and displaying data and comparing two sets of data.

Numbers are split into categories of the first digit(s) and the last digits(s)

e.g. Given the following test scores:

06, 24, 43, 23, 12, 34, 21, 08, 15, 47, 40, 20, 12, 05, 19, 28, 34, 23, 39, 34

Let the stem be the first digit (the tens column). Enter each of the second digits (the units column) into the leaf part of the diagram.

 0 6 8 5 1 2 5 2 9 2 4 3 1 0 8 3 3 4 4 9 4 4 3 7 0

Now arrange the leaf digits in order.

 0 5 6 8 1 2 2 5 9 2 0 1 3 3 4 8 3 4 4 4 9 4 0 3 7

Both parts of a stem and leaf diagram can contain more than one digit.

e.g. For numbers such as 3476, the stem could be 34 and the leaf could be 76.

### Back to Back Stem and Leaf Diagrams

This type of stem and leaf diagram is good for comparing two samples or sets of data.

e.g. A class's scores in tests out of 50

 English Mathematics 6 0 7 9 8 5 3 1 1 1 2 2 4 6 1 4 6 7 9 2 3 5 6 8 9 9 2 4 5 8 3 1 4 7 3 5 6 4 3 4 5 0 Units of stem is 10 marks

The way that each set of marks are distributed can be seen clearly on this type of diagram.

Formula for working out the position of the quartiles and median on a stem and leaf diagram

The quartiles and median split a set of values into four equal parts. This is sometimes difficult to work out for even and odd numbers of values. The formulae below ALWAYS work for any number of values

Quartiles

 Quartile depth =

where n is the number of values and when  is found any halves are dropped.

Therefore, the lower quartile is the 3rd value from the bottom of the set of values.
The upper quartile is the 3rd value from the top of the set of values.

Median
 Median depth =

Therefore the median is the 6th value from either the top or from the bottom of the set of values.
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