# Upper and lower bounds

**Discrete and continuous quantities**

Numerical data can be **discrete** or **continuous**.

**Discrete** data can only take certain value:

For example, jeans sizes, the number of children in a school and the amount of apples

**Continuous** data is from measuring and can be any value within a given range

For example, the weight of a apple, the time it takes for workers to get to work, and the heights of 16 year-olds.

**Upper and lower bounds for discrete data**

Discrete data can have upper and lower bounds. For example, the population of France is 59 million to the nearest million.

What is the lowest number (the lower bound) could be?

The *least* this number could be before being rounded *up* is: 58,500,000

What is the highest number (the upper bound) this could be?

The *most* this number could be before being rounded *down* is: 59,499,999

This is therefore an inequality as the actual population of France is between 58,500,000 and 59,499,999. This can also be written as:

58 500 000 ≤ population < 59 500 000

**Upper and lower bounds for continuous data**

The height of the Burj Khalifa is 828 meters to the nearest meter.

What is the least this measurement before being rounded up? – 827.5 m

What is the most this measurement could be before being rounded up? – 828.5 m

The upper bound and lower bounds are written as follows:

827.5 m (lower bound) ≤ height < 828.5 m (upper bound)