Quartiles, Interquartile Range, and Box Plots

Objective: Read the interquartile range from stated quartiles.

Prerequisite skills: sorted data and medians. The first and third quartiles bound the middle half of the ordered data under a chosen quartile convention. Their difference is the interquartile range, which describes spread without depending on the extreme endpoints. Common error: using maximum minus minimum as the IQR. Restrictions and interpretation: This course uses medians of the lower and upper halves excluding the overall median for odd counts; supplied box-plot quartiles take precedence.

Objective: Use the specified median-of-halves convention.

For an even data count, split the sorted list into equal lower and upper halves. Find each half median for Q₁ and Q₃. Different software can use different conventions, so use quartiles supplied by the question when available. Common error: including an overall odd-count median in both halves without a stated convention. Restrictions and interpretation: This course uses medians of the lower and upper halves excluding the overall median for odd counts; supplied box-plot quartiles take precedence.

Objective: Apply a stated IQR-based outlier rule.

A common descriptive convention flags values below Q₁−1.5IQR or above Q₃+1.5IQR. This rule is an editorial extension, not a claim that every SAT problem requires computing fences. A flagged value is not automatically an error. Common error: adding 1.5 to Q₃ rather than 1.5 times the IQR. Restrictions and interpretation: This course uses medians of the lower and upper halves excluding the overall median for odd counts; supplied box-plot quartiles take precedence. Desmos and method choice: Use Desmos for arithmetic or a graph/table check when that reduces work. Enter parentheses explicitly and verify the requested quantity and units. Use the algebraic steps shown here for an exact result; a rounded graph display is not proof of exact equality.