Mathematics Year 7: What kind of variable is it? Nominal, ordinal, discrete or continuous
Mathematics, Year 7 (Portugal): Sort what varies in a statistical question into four kinds, and choose a question and a precision that give the data you need.
Four kinds of variable
In a statistical question, what changes from one element to the next is the variable. If the answers are categories, it is qualitative: nominal when the categories only have names (how you travel: on foot, bus, bicycle), ordinal when they have a natural order (an opinion: not at all, a little, a lot). If the answers are numbers, it is quantitative: discrete when you count and the values jump (5, 6, 7 stops), continuous when you measure and any value in between is possible.
The kind tells you what you can do with the data
With a nominal variable you can only count how many fall in each category. With an ordinal one you can also say which comes before. With a quantitative one, calculations make sense. That is why the question matters: ask yourself “What do I want to know? Which data answer it?” Precision matters too: to study the trip to school, ask for minutes, not “short” or “long”, or you lose the chance to calculate anything.
One study, four variables
Study: how do Year 7 students get to school? (1) “How do you travel?” — on foot, bus, bicycle, car: names, no order, so qualitative nominal. (2) “The bus wait is: too short / fine / too long”: categories with an order, so qualitative ordinal. (3) “How many stops does your bus have?” — 6, 7, 8: you count, and there is no 6.5 stops, so quantitative discrete. (4) “How many minutes does the trip take?” — 12 min, 13 min, and 12.5 min fits between them: measured, so quantitative continuous.
A number is not always a quantity
Many people think: “if the answer is a number, the variable is quantitative”. But a player's shirt number (7, 10, 23) is only a name written with digits: adding 7 and 10 tells you nothing, and player 10 is not “worth more” than player 7. It is qualitative nominal. The same goes for phone numbers and postcodes. A quick test: do calculations with these values mean anything? If not, they are names.
Forms, surveys and apps
You meet all four kinds in forms and surveys: the name of a class (nominal), “liked it a lot / liked it / did not like it” (ordinal), the number of messages received today (discrete), the minutes spent on a phone (continuous). Before you write a question, decide which kind of variable you will get, and whether the answer can be given with the precision you need.
Test what you learned
Which of these is a qualitative ordinal variable?
- a) Colour of a student's backpack
- b) Tiredness at the end of the day: none / some / a lot
- c) Number of messages received today
- d) Time a student takes to run 100 m, in seconds
Correct answer: b) Tiredness at the end of the day: none / some / a lot — Right: the answers are categories with a natural order, none < some < a lot. It is qualitative ordinal.
A questionnaire records five variables: eye colour, distance from home to school in km, number of bus stops, tiredness (none / some / a lot) and trip time in minutes. How many are quantitative?
- a) 1
- b) 2
- c) 3
- d) 4
Correct answer: c) 3 — Right: distance (continuous), stops (discrete) and time (continuous). Eye colour is nominal and tiredness is ordinal.
In a football team, the shirt numbers are 1, 4, 7, 10 and 23. What kind of variable is “shirt number”?
- a) Qualitative nominal: the number only names the player
- b) Quantitative discrete: they are whole numbers
- c) Qualitative ordinal: 10 comes after 7
- d) Quantitative continuous: there are numbers between 7 and 10
Correct answer: a) Qualitative nominal: the number only names the player — Right: adding shirt numbers or saying 10 is “more” than 7 means nothing. The number is just a name written in digits.
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