Uvero — STEM Learning

Quartiles and Box Plots

Quartiles split ordered data into four parts and the interquartile range $Q_3-Q_1$ measures middle spread. Box plots compare centre and spread while reducing outlier influence. At Grade 10, fluent symbolic work must stay connected to graphs, tables, diagrams and real quantities.

Worked reasoning

Use $Q_3-Q_1$ .
$27-12=15$ .

If $Q_1=12$ and $Q_3=27$ , find the IQR.

Which statement best captures the central mathematical idea in Quartiles and Box Plots?

Box plots compare centre and spread while reducing outlier influence.

A memorised rule may be used without checking signs, domains, units, graph family or geometric hypotheses.

A memorised formula is valid even when its conditions are not met.

The diagram or notation replaces the need to justify each mathematical step.

When starting a problem about Quartiles and Box Plots, which move is most reliable?

Identify the mathematical family, list the given quantities and state the domain or geometric conditions for quartiles and box plots.

Round every value before identifying the mathematical structure.

Choose the longest available formula and substitute immediately.

Assume the desired conclusion and work backwards without checking equivalence.

Which statement is a misconception that must be rejected when working with Quartiles and Box Plots?

A memorised rule may be used without checking signs, domains, units, graph family or geometric hypotheses.

Box plots compare centre and spread while reducing outlier influence.

Identify the mathematical family, list the given quantities and state the domain or geometric conditions for quartiles and box plots.

Use substitution, a second representation or a magnitude estimate to verify the result.