Classifying Data

Data is just the answers you collect when you ask a question. Ask your class what their favourite fruit is and the answers come back as words — apple, banana, orange. Ask how many pets they have and the answers come back as amounts — nought, two, one, three. Those two kinds of answer have names. Words that sort people into groups are called categorical data. Amounts you counted or measured are called numerical data. Every set of data you meet in this chapter is one of these two, so the very first thing to do is look at the answers and decide which one you have. That choice decides which table and which graph you are allowed to use later on.

Categorical data puts each person or thing into a named group. Favourite fruit, eye colour, how you get to school, the type of pet you own — all of these give you groups rather than amounts. The one thing you cannot do with categories is arithmetic. You cannot add apple to orange, so saying the average favourite fruit is banana is nonsense. What you can do is count how many landed in each group. Out of twenty students, seven chose apple, six banana, four orange and three grapes, and those four counts tell you everything. You can also name the most popular group, which here is apple. Counting and comparing groups is exactly what categorical data is for.

Numerical data is an amount you counted or measured. The number of pets you own, your height in centimetres, a test score out of twenty, the minutes you spent on homework — each of these is a genuine quantity. The proof is that arithmetic works on them. Take five test scores of 12, 15, 18, 11 and 14. Add them and you get 70, then share that between the five students and you get 14, so the average score is 14 marks. That sentence is useful and true. Try the same with eye colours and you get nowhere. So here is the test to remember: if doing arithmetic on the values makes sense, the data is numerical; if it is nonsense, the data is categorical.

Here is the trap that catches almost everybody. Some data is written with digits but is not numerical at all. A jersey number names a player, a postcode labels a suburb, a phone number labels a house, and a bus route number names a route. Try the arithmetic test on them and it falls apart immediately: player seven plus player nine does not give you player sixteen, and the average postcode of your class tells you nothing whatsoever. These numbers are labels — they name things rather than measure things — so they are categorical, even though they look like numbers on the page. Whenever you see digits, do not assume. Ask whether adding or averaging them would mean anything, and let that decide.

Numerical data splits one step further, and the question is simply whether you counted it or measured it. If you counted — one pet, two pets, three pets — the data is called discrete, because it only lands on whole steps and nobody owns two point four pets. If you measured it with a ruler, some scales or a clock, the data is called continuous, because any value in between is possible and a height really can be one hundred and fifty-two point four centimetres. Both kinds are still numerical; this is just a finer sort inside that group. So every set of data you meet gets classified twice: first categorical or numerical, and then, if it is numerical, counted or measured.