### 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 = 15th 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 = 15th value = 37
The mean of class 1 = 45.2

The mode of class 2 = 35
The median of class 2 = 30/2 = 15th value = 38
The mean of class 2 = 46.6

1. 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.
2. 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.

### Resources at Fingertips

This is a vast collection of tutorials, covering the syllabuses of GCSE, iGCSE, A-level and even at undergraduate level. They are organized according to these specific levels.
The major categories are for core mathematics, statistics, mechanics and trigonometry. Under each category, the tutorials are grouped according to the academic level.
This is also an opportunity to pay tribute to the intellectual giants like Newton, Pythagoras and Leibniz, who came up with lots of concepts in maths that we take for granted today - by using them to serve mankind.

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