Missing Data — Fundamental Concepts

Fundamental Concepts

Begin with the stated relationships

A row containing 18, a blank and 27 with a total of 70 gives 18 + x + 27 = 70, so x = 25. The row total supplies the constraint. Without it or another independent relationship, the missing entry would not follow from the neighbouring values alone.

Convert aggregates carefully

An average of 24 across five entries means a total of 120. Subtract the four known entries to recover the fifth. A percentage condition must name its base: if a cell is 30% of a row total of 200, its value is 60. If the total is itself unknown, retain it as a variable rather than using an unrelated column total.

Count independent information

The equations x + y = 80 and 2x + 2y = 160 give the same information. They do not determine x and y separately. Yet the requested quantity x + y is known. A second independent condition, such as x − y = 10, would determine both entries.

Check feasibility and precision

Counts ordinarily require non-negative integers, whereas measured quantities may be fractional. A negative inferred attendance count can reveal inconsistent inputs or a mistaken equation. Rounded percentages may define an interval rather than an exact missing count. Preserve that uncertainty instead of presenting the centre of a possible range as uniquely established.