Definition

Qualitative, discrete and continuous data

Statistics • Data Classification

Statement

Data are qualitative (equivalently categorical) when each observation is an attribute such as colour, brand or blood group, and quantitative when each observation is a number. Quantitative data are discrete when the variable can take only isolated values, typically counts

0, 1, 2, \dots

, and continuous when it can take every value in an interval, as a measured length, mass or time can.

How to use it

1Ask first whether the observations can sensibly be added or averaged; if not, the data are qualitative.
2For numerical data, ask whether a value strictly between two neighbouring observations is possible: if not, the variable is discrete.
3Anything recorded as 'how many' is discrete; anything recorded as 'how much' is continuous, however coarsely it happens to be rounded.

Worked example

Classify each variable: (i) the eye colour of a pupil, (ii) the number of goals a team scores, (iii) the time a runner takes.

Step-by-step

1
$(i) eye colour is an attribute, not a number$
Why: Qualitative, equivalently categorical.
2
$(ii) goals are a count : 0, 1, 2, \dots$
Why: Quantitative and discrete: no value lies strictly between $2$ and $3$ goals.
3
$(iii) a time may take any value in an interval$
Why: Quantitative and continuous; rounding the record to hundredths does not make the variable itself discrete.

Answer

(i) qualitative, (ii) discrete, (iii) continuous

Watch out

'Qualitative' and 'categorical' are two names for one thing, so neither can be the single correct answer when both are offered. A numerical code standing for a category, such as

1

for male and

2

for female, does not make the data quantitative.

Also known as

types of data, discrete data, continuous data, categorical data, qualitative versus quantitative

Qualitative, discrete and continuous data

Statement

Worked example

Appears in past papers

2018 (II)

2016 (II)