Handling data --- Data --- Pictograms --- Graphs --- Mean, median, mode --- Sorting

Before handling data, such as making a pictogram graph, you need to gather the data. Here are some ideas for teachers.

Pictogram graphs need simple numbers, not too big and preferably whole numbers to start with. The obvious place to start in a school is data about the children themselves. They could count how many come to school by coach, or by car, or walking, for example. Or you could find out who has a birthday in winter, spring, summer or autumn (fall), and add those up. You could count how many children have different types of pets. You could also use other types of data, such as weather temperatures, if they are within a reasonable range. Be careful what sort of data you collect. If you choose a personal measurement such as height or weight, some people may be embarrassed or even ashamed to be compared with others. Other data such as hair or skin colour may not show enough range and may have racial overtones. In some cases, you may even fall foul of privacy or data protection laws.

When considering what data to use, I would advise that the teacher tries making a graph surreptitiously first with some data, to see where the problems will be with the final graph.

Most data collection is just writing numbers down. You ask the class a question, and a number of hands shoot up in the air, and you count them and write the number down. If children are gathering their own data, then they will be wandering around asking various people individually, which means that they can't count a group, and write a single number down. Instead, one person will say they belong in one group, and another in a different group, and all this has to be recorded as it happens. Or if you are conducting a traffic survey then you need to count the different sorts of traffic as they pass. The best way to do this count is by using tallies, or tally marks. Imagine that you are counting cars. As the first four cars pass, you write a one down, so at the fourth, you have four ones. Then for the fifth, you cross, the four out, looking rather like a bar gate. The sixth to ninth are marked as another group of ones, next to the first group, and the tenth is the second group crossed out. When you need to tot them up, you count the crossed-out groups as fives, and add on any uncrossed-out ones.

Click on *Count tallies* to watch how tallies work, or enter a number up to 100.

Tallies are an interesting system. They are a unary system, since you use several ones to show larger numbers. It is base 5, as that is where you cross the units out. But there is nothing larger than 5. You just carry on (and on, and on) putting groups of 5s. For a very large number, the tallies would take an enormous amount of room. This doesn't matter as tallies are only used for small counts. There is no zero.

© Jo Edkins 2006 - Return to Numbers index