Solving data problems
Problems about data handling often ask for the mean (average), mode (most common), median (middle value) or range (biggest − smallest). Use the four steps: understand, plan, solve, check. First decide which of these the question is really asking for, because each one is worked out in a different way.
Key idea
Mean = sum of all values ÷ how many values. Range = largest − smallest.
Worked example
Worked example
Ali's marks in 5 tests are 6, 8, 7, 9, 5. Find the mean.
Understand: there are 5 marks and we want the average.
Solve: sum = 6 + 8 + 7 + 9 + 5 = 35.
Mean = 35 ÷ 5 = 7.
Check: 7 is between the smallest (5) and largest (9), so it is a sensible answer. ✓
For the same marks, the range = 9 − 5 = 4.
Remember
- Add first, then divide, for the mean.
- Put numbers in order before finding the median.
- Mode is the value that appears most often.