Upper Bound - GCSE Maths Definition

In GCSE Mathematics, an upper bound is the largest value that a quantity can take, often within a given range. Having said that, and due to the way we write inequalities in mathematics, the upper bound is not actually included - this is demonstrated in the example below.

For grouped data, we may have the class interval . The upper bound is 40, but due to the inequality sign being <, a value of exactly 40 is not actually included in the interval, just every value up to it. 40 would still be called the upper bound.

Similarly, upper bounds also occur when we are considering where rounded numbers come from. For example, if a value has been rounded to the nearest whole number, to get 8, then all values between 7.5 and, but not including 8.5, could be the original value before it was rounded. We would write this interval as 7.5 ≤ x < 8.5 and 8.5, although not strictly included, would still be referred to as the upper bound.