Upper & Lower Bounds

Bounds & Error Intervalsvideo

Bounds & Error Intervals

What are bounds?

• Bounds are the values that a rounded number can lie between

  • The smallest value that a number can take is the lower bound (LB)

  • The largest value that a number must be less than is the upper bound (UB)

• The bounds for a number, $x$, can be written as $\mathrm{LB}\le x<\mathrm{UB}$

  • Note that the lower bound is included in the range of values $x$ but the upper bound is not

How do we find the upper and lower bounds for a rounded number?

• Identify the degree of accuracy to which the number has been rounded

  • E.g. 24 800 has been rounded correct to the nearest 100

• Divide the degree of accuracy by 2

  • E.g. If an answer has been rounded to the nearest 100, half the value is 50

• Add this value to the number to find the upper bound

  • E.g. 24 800 + 50 = 24 850

• Subtract this value from the number to find the lower bound

  • E.g. 24 800 - 50 = 24 750

• The error interval is the range between the upper and lower bounds

  • Error interval: LB ≤ x < UB

  • E.g. 24 750 ≤ 24 800 < 24 850