Charts with missing values that must be deduced algebraically.

In a missing data set, some entries of a table or chart are blank. The remaining values, together with totals, averages, ratios, or percentages stated in the question, give enough relationships to recover them.

Finding what is missing

• Totals: a missing part = total - sum of the known parts.
• Averages: total = average x number of items, then subtract the known values.
• Percentages: all shares add to 100% in a pie chart; a known value and its percentage give the whole.
• Ratios: if two values are in the ratio a : b, then one is a/b times the other.
• Percentage change: new = old x (1 + change / 100).
• Two unknowns: write two equations and solve them by elimination or substitution.

How to solve questions

1. List the known values and the extra information given.
2. Represent each missing value with a letter if needed.
3. Write an equation from each relationship (sum, average, ratio, or percentage).
4. Solve for the unknowns, starting with the simplest equation.
5. Check by confirming that the completed table satisfies every given condition.