The big picture
One table, and three averages from it.
| Idea | Remember | Example |
|---|---|---|
| Classes | No gaps. Here, equal width. A boundary reading goes up. | 10 is in 10-20. |
| Class mark | Bounds added, then halved. | (10 + 20) ÷ 2 = 15. |
| Direct mean | Σ f x ÷ Σ f. | 320 ÷ 20 = 16. |
| Assumed mean | a + Σ f d ÷ Σ f. | 25 − 4 = 21. |
| Step deviation | a + h × Σ f u ÷ Σ f. | 25 + 10 × (−0.4) = 21. |
| Median | Count to n ÷ 2, then the formula. | 30 + 4 = 34. |
| Mode | Tallest class and its neighbours. | 30 + 4 = 34. |
| Choosing | A few huge values pull the mean up far more than the median. | 15 and 12.5. |
| Full run | Mean, median, mode from one table. | 13.2, 13.75, 16.25. |
| Missing frequency | Write the mean with f in it. Set it equal to the given mean. Solve for f. | (460 + 25f) ÷ (16 + f) = 28 gives f = 4. |
| Two missing | Use the total to link x and y. Use the median to find x. Then find y. | x = 10, y = 8. |
| Close the gaps | Half the gap goes to each side. Lower limits go down. Upper limits go up. | 11-17 becomes 10.5-17.5. |
| Below tables | Each class holds its own total minus the total before it. | 24 − 12 = 12. |
This is Chapter 13, Statistics. Open its exercises. For each table, ask which average answers the question.
Every table here was made up. The method stays the same for real data.