Data can either be discrete or continuous.

• Discrete data consists of integers, units of measurement cannot be split. Only certain values have a meaning.
• Continuous data can be shown on a number line, all points on this line have a meaning. In between two measurements there's always a valid "middle" measurement. So for example, between 156.3cm and 156.4cm there's 156.35cm.

a)

Height is a continuous variable. For example, 180.3cm and 180.4cm have a valid midpoint 180.35cm. Hence, this data is continuous.

b)

The number of chocolate bars sold on Monday will always be an integer. There is no middle measurement between 1 and 2 bars sold. You cannot buy a half of a bar. Therefore, this is a discrete set of data.

c)

Shoe sizes are a discrete set of data. For example, sizes 39 and 40 mean something while the middle value 39.5 does not..

d)

Time is a continuous variable. For example, 54.2s and 54.3s have a valid midpoint 54.25s. Hence, this data is continuous.

e)

When we round continuous variables to the nearest integer, this data becomes discrete, as there are no valid middle measurements between the integers. Therefore, the time taken to run 10km to the nearest min is discrete and not continuous.

f)

The result of rolling 3 dice can take values of integers from 3 up to 18. For example, values 3 and 4 do not have any valid middle measurement. Therefore, this is a discrete set of data.