Collecting and Classifying Data

Data comes in two kinds. Categorical data sorts things into groups — eye colour, favourite sport, mode of transport. You can count how many fall in each group, but you cannot average it, because 'the average eye colour is blue' means nothing. Numerical data measures or counts an amount — height, mass, test score, number of siblings — and averaging it is meaningful. Be careful with data that looks numerical but is not: jersey numbers, postcodes and phone numbers are all digits, yet the average postcode of a class is meaningless. The test to apply is whether doing arithmetic on the values makes sense. If it does not, the data is categorical.

Numerical data splits further. Discrete data is counted and takes separate whole values — number of siblings, goals scored, pets owned. Nothing sits in between, because you cannot have 2.4 siblings. Continuous data is measured and can take any value in a range — height, mass, time, temperature. A height can genuinely be 158.34 centimetres. The test is whether you counted it or measured it with an instrument. Shoe size is the odd case: it is measured, but only certain sizes exist, so it behaves as discrete. Similarly, age in whole years is discrete while exact age is continuous. This split matters later, because it decides which graph you are allowed to use.

When you collect data you either ask everyone or ask some. A census covers every member of the group, so it is accurate with no guessing — practical for one class, but slow and expensive for a whole country. A sample covers a smaller part, which is fast and cheap but only an estimate, and it is only useful if the sample represents the group. That word matters, because a biased sample gives a wrong answer no matter how big it is. Surveying only the basketball team about favourite sport is biased. So is surveying only your friends, or asking online about internet use, which misses everyone not online. The fix is a random sample, where everyone has an equal chance of being chosen.

Even with a perfect sample, the question itself can bias the answer. A leading question pushes people towards a reply — 'Don't you agree homework is too much?' should be 'How much homework do you get each night?'. A vague question invites inconsistent answers, so 'Do you exercise often?' becomes 'How many days a week do you exercise?'. A two-in-one question is unanswerable if someone likes maths but not science, so split it. And missing options force people into the wrong box — 'Do you walk or drive?' needs bus, train, cycle and other. A good question is neutral, specific, asks one thing, and covers every possible answer.

The rest of this chapter follows one process. Step one: ask a clear question, like 'Do Year 8 students sleep 8 hours a night?'. Step two: collect the data, using a census or a random sample and fair questions. Step three: organise it into a frequency table, grouping the values if there are many. Step four: display it with the right graph for that data type. Step five: analyse and conclude, using averages, spread and shape — and then actually answer the question you asked. That last point is where marks are lost most often. A graph on its own is not a conclusion; you have to say what it tells you about the original question.