MYP Extended Mathematics Topic Upper and Lower Bounds…

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MYP Extended Mathematics Topic Upper and Lower Bounds… | RevisionDojo

Lower and Upper Bounds in Measurement

Definition

Lower bound

The lower bound of a rounded or measured quantity is the smallest value the original (exact) quantity could have had, given the stated accuracy.

Definition

Upper bound

The upper bound of a rounded or measured quantity is the largest value the original (exact) quantity could have had, given the stated accuracy. For continuous data, the true value is strictly less than this upper bound.

From a Single Number to an Interval

When a value is reported as a rounded measurement (for example, “16 m to the nearest metre”), the true value is not exactly known.
Instead, it lies in an interval of possible values.
1. The lower bound is the smallest possible value.
2. The upper bound is the largest possible value (not included for continuous data).
Together, these are called the limits of accuracy.

Continuous Measurements Create Ranges, Not Single Values

Many real measurements are continuous: they can take any value in an interval (for example, height, mass, time, temperature).
This is different from discrete quantities, which come in fixed steps (like number of students in a class).
Because continuous measurements are recorded to a stated accuracy (nearest metre, nearest 0.1 kg, 2 significant figures, etc.), you should treat the recorded number as a label for an interval of possible true values, not as an exact value.

Analogy

Think of the rounded value as the name of a whole neighbourhood of numbers.

The lower bound is the first house in the neighbourhood.
The upper bound is just before the last house.

How to Find Bounds from a Rounded Value

Rounding works by grouping values around a midpoint.
Suppose a measurement is rounded to the nearest unit of size $a$.
Examples of step size $a$:
1. Nearest 10 → $a=10$
2. Nearest 0.1 → $a=0.1$
3. Nearest 0.01 → $a=0.01$
Then the half-step is $\frac{a}{2}$.
If the recorded (rounded) value is $x$, then
1. Lower bound = $x−\frac{a}{2}$
2. Upper bound = $x+\frac{a}{2}$

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MYP Extended Mathematics Upper and Lower Bounds Notes

Lower and Upper Bounds in Measurement

From a Single Number to an Interval

Continuous Measurements Create Ranges, Not Single Values

How to Find Bounds from a Rounded Value

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Lower and Upper Bounds in Measurement

From a Single Number to an Interval

Continuous Measurements Create Ranges, Not Single Values

How to Find Bounds from a Rounded Value

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Advanced Number and Bounds3 subtopics

Inequalities and Modelling1 subtopic

Function Transformations4 subtopics

Advanced Probability1 subtopic

Geometric Transformations1 subtopic

Variation and Standard Deviation3 subtopics

Trigonometric Functions and Rules4 subtopics

Sequences, Rational Expressions and Equations5 subtopics

Covariance and Correlation3 subtopics

Logarithms and Non-Linear Inequalities3 subtopics

Graph Theory and Vectors4 subtopics

MYP Extended Mathematics Upper and Lower Bounds Notes

Advanced Number and Bounds3 subtopics

Inequalities and Modelling1 subtopic

Function Transformations4 subtopics

Advanced Probability1 subtopic

Geometric Transformations1 subtopic

Variation and Standard Deviation3 subtopics

Trigonometric Functions and Rules4 subtopics

Sequences, Rational Expressions and Equations5 subtopics

Covariance and Correlation3 subtopics

Logarithms and Non-Linear Inequalities3 subtopics

Graph Theory and Vectors4 subtopics

Lower and Upper Bounds in Measurement

From a Single Number to an Interval

Continuous Measurements Create Ranges, Not Single Values

How to Find Bounds from a Rounded Value

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Unlock the rest of this chapter with a free account

Lower and Upper Bounds in Measurement

From a Single Number to an Interval

Continuous Measurements Create Ranges, Not Single Values

How to Find Bounds from a Rounded Value

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Unlock the rest of this chapter with a free account