### Stem and Leaf Diagrams

Stem and Leaf diagrams provide a way to show data as it is done in tables and charts. It is ideal to represent a large number of data so that we can get a clear idea about the spread and peaks
at a glance. In addition, the averages can be calculated speedily too.

The Marks for English Literature in a certain GCSE class is as follows; the corresponding stem and leaf diagram is on the right:

15,32,39,54,55,79
77,99,52,37,34,56
35,13,18,19,90,59
12,34,37,75,53,34
10.59,70,95,33,12

**4|3 means 43**
The mode of the data = 34

The median of the data = 30/2 = 15^{th} value = 37

The mean of the data = 45.2

The above Stem and Leaf diagram can be extended to show two different sets of data on either side - of the stem. The it is called **Back-to-Back Stem and Leaf Diagram**.

E.g.

The Marks for English Literature in two GCSE classes are as follows; the corresponding Stem and Leaf diagrams are on the right:

**Class 1 - ***on the right*

15,32,39,54,55,79
77,99,52,37,34,56
35,13,18,19,90,59
12,34,37,75,53,34
10.59,70,95,33,12

**Class 2 -***on the left*

16,33,38,55,56,78
78,98,53,36,35,57
36,14,19,18,91,58
13,35,38,76,54,35
11.58,71,96,34,13

**2|4|3 means 42 on the left and 43 on the right**
The mode of class 1 = 34

The median of class 1 = 30/2 = 15^{th} value = 37

The mean of class 1 = 45.2

The mode of class 2 = 35

The median of class 2 = 30/2 = 15^{th} value = 38

The mean of class 2 = 46.6

#### Stem and Leaf Diagrams - interactive practice

With the following applet, you can practise stem and leaf diagrams interactively. All you have to do is clicking the button to generate a random set of data.

#### Practice Questions

- The temperature in March, in Middlesex area is as follows:

12, 9, 9, 21, 10, 7, 8, 11, 10, 15, 14, 13, 12,9, 14

11, 10, 19, 11, 20, 17, 18, 11, 10, 13, 12, 11, 12,9, 11

Construct a Stem and Leaf diagram to find the averages of the data.
- The heights of two sets of plants - one grown with a special fertilizer and the other one without - are as follows:

**Set A**

23, 32, 42, 14, 16, 32, 33, 16, 15, 22, 51, 28, 56, 27, 29

26, 38, 13, 24, 26, 11, 15, 19, 18, 32, 46, 52 26, 57, 59

23, 32, 42, 24, 16, 22, 33, 26, 15, 22, 51, 28, 56, 27, 29

46, 38, 13, 24, 26, 21, 35, 19, 48, 32, 46, 22 26, 57, 59

**Set B**

13, 32, 32, 14, 16, 32, 33, 26, 25, 22, 51, 28, 56, 27, 29

26, 38, 13, 24, 26, 11, 55, 29, 18, 32, 46, 52 46, 57, 59

23, 32, 42, 24, 26, 22, 33, 26, 15, 22, 51, 38, 46, 27, 29

46, 38, 13, 24, 16, 21, 35, 29, 48, 42, 46, 22 26, 57, 59

Construct a back-to-back Stem and Leaf diagram to calculate the averages for both groups.