Missing Data — Revision Notes

⚡ 30-Second Revision

Blank does not mean zero.
Translate totals and averages into equations.
Check percentage denominators.
Repeated equations add no independent constraint.
The target may be known even if components are not.

2-Minute Revision

Use variables for missing entries and equations for supplied relationships. Recover a total from an average before subtracting known values. Check whether multiple conditions are genuinely independent and whether the target, rather than every variable, is uniquely determined. Domain restrictions and rounding affect what can be concluded. Verify the result by substitution; if two admissible assignments give different target values, report insufficiency.

5-Minute Revision

Three departments have counts 24, x and y, with a combined total of 90. Thus x + y = 66. This determines the average count of the last two departments as 33, but not either count individually. The pairs (30, 36) and (20, 46) both fit. If a second independent condition says y is 6 more than x, then x = 30 and y = 36. Explain why knowing the average of the last two adds no information beyond their already known sum.

Vyyuha Quick Recall

Target → Variables → Independent equations → Check. Solve what the evidence determines.