### Overview Maths GCSE Interpreting and Representing Data

Someone once said “there are lies, damned lies and statistics”. Understanding how to interpret and represent data gives you a chance of identifying when companies, politicians, employers (in fact anyone in authority) are using statistics in a less than honest way.

To be more positive the interpretation and representation of data enables you to identify and solve real-life problems. There are a number of techniques. None of these techniques is particularly difficult, you just have to practice to learn them. As usual the best way for me to make sure I remember each technique is to:-

a) Devise a question

b) Explain the approach required to answer the question.

c) Answer the question in detail.

I find that if I have to understand a technique well enough to set a question and explain how to answer it then I have a good chance of remembering that technique. In addition, if my children ask me a question about it in the future, I will not only be able to give them the answer but also show them how to answer the question for themselves.

## Stem-and-leaf Diagrams

I had heard of stem-and-leaf diagrams but I soon realised that I didn’t know or remember how they worked. They are a simple but impressively effective way to quickly organise large amounts of data.

Question

Tom believed that his parents did not give him enough pocket money. He decided to ask his classmates how much pocket money per week they received. This table shows the data he collected:-

a) Use this data to prepare a stem-and-leaf diagram

b) How many of Tom’s classmates receive more than £5 pocket money per week?

Approach

There is no point trying to describe a stem-and-leaf diagram, just take a peek at the answer below! Some key points to bear in mind.

- Keep it as simple as possible. The left hand column (the stem) typically has the largest single unit of measure (in this example £‘s).
- Don’t try to write the figures in the right-hand columns (the leaves) in ascending order as this may take too long and could easily result in mistakes. The idea of a stem-and-leaf diagram is to quickly sort a mass of data into a manageable table.
- Check the total number of entries in your answer is the same as the total number of data points from the original list.
- Make sure you include a key to show how the diagram should be read (see example in answer below).

Answer

a) Stem-and-leaf diagram of Tom’s data:-