Follow the labelled points

A line chart connects values across an ordered variable, usually time. The line between points helps show a trend but does not always authorise reading an unstated intermediate value. Identify the horizontal unit, vertical unit and each series label. For two series, trace one colour or line style at a time. A rise between consecutive points is a difference; a percent rise divides that difference by the earlier point.

Trend questions need precise language

“Highest value” asks for the largest plotted point. “Greatest rise” asks for the largest positive adjacent difference, which may occur on a line whose highest value is elsewhere. “Steepest percentage rise” compares proportional changes, not absolute slopes alone. If values move from 20 to 30 and from 200 to 220, the second has a bigger unit rise (20) but the first has a bigger percent rise (50% versus 10%).

Aggregate across periods

To find a total over five years, add the five labelled points; do not multiply the last point by five. To find the mean, divide that total by five. If a question compares two series over a range, use the same years for both. When the graph scale is dense, write a short two-column list of only the needed points. In review, trace the correct series with your finger and state whether the error was series identity, interval, unit or base.

Endpoint change and intermediate movement

A five-year line may read 40, 55, 50, 80 and 70. The overall change from Year 1 to Year 5 is 70−40=30, although the line rises and falls along the way. The largest one-year increase is 80−50=30, from Year 3 to Year 4. The largest one-year fall is 80−70=10, from Year 4 to Year 5. The end-to-end change and the largest adjacent change happen to share a number here, but they answer different questions. Always mark the named endpoints.

The five-year total is 40+55+50+80+70=295, and the mean is 59. Neither is the value at any one year. If a question asks for the percentage increase from Year 1 to Year 5, divide 30 by the starting 40 to get 75%. A percentage change from Year 5 back to Year 1 would divide the 30-unit fall by 70, about 42.9%. Direction changes the denominator.

Do not overread a connecting line

The segment between Year 2 and Year 3 makes the trend visible, but a line chart with annual observations does not prove the exact value halfway through that interval. Interpolation is only justified if the question or model permits it. The visual height can also be misleading if the vertical axis begins above zero. Use the point labels when printed, then use the grid for a rough check. For two-line graphs, first locate the right legend colour or line style; then compare values at the same year.

Quick trend language

“Increasing throughout” requires every adjacent step to rise. “Overall increase” only compares first and last. “Peak” asks for the highest labelled point, while “steepest rise” asks for the largest adjacent difference, not simply the highest point. Practice rewriting each phrase as a calculation before inspecting options. If the graph shows a ratio between two series, make sure both series have the same unit and axis before dividing their values.

Practice — 50 questions

Attempt every item before reading the answers. Use the chart or caselet printed with the question.

1. What is the absolute change from Year 1 to Year 5?

A. 5 B. 0 C. 15 D. 10

2. What is the combined value for Year 2 and Year 3?

A. 140 B. 145 C. 135 D. 150

3. What is the peak labelled value across the five years?

A. 125 B. 115 C. 110 D. 120

4. What is the lowest labelled value across the five years?

A. 95 B. 100 C. 105 D. 90

5. What is the five-year total?

A. 425 B. 430 C. 435 D. 420

6. What is the absolute change from Year 1 to Year 5?

A. 15 B. 10 C. 5 D. 20

7. What is the combined value for Year 2 and Year 3?

A. 250 B. 260 C. 255 D. 245

8. What is the peak labelled value across the five years?

A. 110 B. 105 C. 120 D. 115

9. What is the lowest labelled value across the five years?

A. 65 B. 50 C. 60 D. 55

10. What is the five-year total?

A. 480 B. 470 C. 485 D. 475

11. What is the absolute change from Year 1 to Year 5?

A. 55 B. 60 C. 65 D. 70

12. What is the combined value for Year 2 and Year 3?

A. 170 B. 155 C. 165 D. 160

13. What is the peak labelled value across the five years?

A. 95 B. 100 C. 90 D. 85

14. What is the lowest labelled value across the five years?

A. 35 B. 45 C. 50 D. 40

15. What is the five-year total?

A. 340 B. 335 C. 330 D. 325

16. What is the absolute change from Year 1 to Year 5?

A. 20 B. 15 C. 25 D. 10

17. What is the combined value for Year 2 and Year 3?

A. 235 B. 225 C. 230 D. 240

18. What is the peak labelled value across the five years?

A. 110 B. 105 C. 115 D. 100

19. What is the lowest labelled value across the five years?

A. 35 B. 40 C. 45 D. 50

20. What is the five-year total?

A. 440 B. 445 C. 450 D. 435

21. What is the absolute change from Year 1 to Year 5?

A. 70 B. 55 C. 60 D. 65

22. What is the combined value for Year 2 and Year 3?

A. 235 B. 245 C. 250 D. 240

23. What is the peak labelled value across the five years?

A. 125 B. 130 C. 135 D. 140

24. What is the lowest labelled value across the five years?

A. 80 B. 85 C. 75 D. 70

25. What is the five-year total?

A. 485 B. 475 C. 490 D. 480

26. What is the absolute change from Year 1 to Year 5?

A. 55 B. 70 C. 65 D. 60

27. What is the combined value for Year 2 and Year 3?

A. 165 B. 160 C. 155 D. 170

28. What is the peak labelled value across the five years?

A. 140 B. 125 C. 135 D. 130

29. What is the lowest labelled value across the five years?

A. 40 B. 45 C. 50 D. 55

30. What is the five-year total?

A. 430 B. 440 C. 425 D. 435

31. What is the absolute change from Year 1 to Year 5?

A. 30 B. 25 C. 20 D. 15

32. What is the combined value for Year 2 and Year 3?

A. 110 B. 105 C. 115 D. 120

33. What is the peak labelled value across the five years?

A. 125 B. 130 C. 135 D. 120

34. What is the lowest labelled value across the five years?

A. 45 B. 60 C. 50 D. 55

35. What is the five-year total?

A. 365 B. 355 C. 360 D. 370

36. What is the absolute change from Year 1 to Year 5?

A. 20 B. 15 C. 25 D. 30

37. What is the combined value for Year 2 and Year 3?

A. 165 B. 180 C. 175 D. 170

38. What is the peak labelled value across the five years?

A. 80 B. 75 C. 70 D. 65

39. What is the lowest labelled value across the five years?

A. 40 B. 50 C. 55 D. 45

40. What is the five-year total?

A. 315 B. 300 C. 310 D. 305

41. What is the absolute change from Year 1 to Year 5?

A. 10 B. 5 C. 15 D. 20

42. What is the combined value for Year 2 and Year 3?

A. 235 B. 220 C. 230 D. 225

43. What is the peak labelled value across the five years?

A. 115 B. 125 C. 120 D. 110

44. What is the lowest labelled value across the five years?

A. 70 B. 75 C. 60 D. 65

45. What is the five-year total?

A. 410 B. 400 C. 415 D. 405

46. What is the absolute change from Year 1 to Year 5?

A. 45 B. 50 C. 55 D. 60

47. What is the combined value for Year 2 and Year 3?

A. 180 B. 175 C. 165 D. 170

48. What is the peak labelled value across the five years?

A. 85 B. 75 C. 80 D. 90

49. What is the lowest labelled value across the five years?

A. 90 B. 100 C. 95 D. 85

50. What is the five-year total?

A. 400 B. 390 C. 385 D. 395

Answers and explanations

Check the value and the unit before comparing your working with the calculation.

1. A. Use Year 1=45 and Year 5=50; absolute change |50−45|=5.

APDI26-06-01 | line-charts | Easy

2. A. Year 2=80 and Year 3=60; total 140.

APDI26-06-02 | line-charts | Easy

3. B. Compare [50, 60, 80, 115, 45]; the peak is 115.

APDI26-06-03 | line-charts | Easy

4. A. Compare [115, 105, 95, 125, 95]; the minimum is 95.

APDI26-06-04 | line-charts | Easy

5. A. Add the five point labels [80, 125, 70, 75, 75]; total 425.

APDI26-06-05 | line-charts | Easy

6. B. Use Year 1=115 and Year 5=105; absolute change |105−115|=10.

APDI26-06-06 | line-charts | Easy

7. A. Year 2=125 and Year 3=125; total 250.

APDI26-06-07 | line-charts | Easy

8. A. Compare [65, 70, 110, 100, 40]; the peak is 110.

APDI26-06-08 | line-charts | Easy

9. D. Compare [75, 55, 70, 75, 100]; the minimum is 55.

APDI26-06-09 | line-charts | Easy

10. D. Add the five point labels [130, 55, 120, 95, 75]; total 475.

APDI26-06-10 | line-charts | Easy

11. B. Use Year 1=60 and Year 5=120; absolute change |120−60|=60.

APDI26-06-11 | line-charts | Easy

12. D. Year 2=105 and Year 3=55; total 160.

APDI26-06-12 | line-charts | Easy

13. C. Compare [70, 90, 85, 55, 70]; the peak is 90.

APDI26-06-13 | line-charts | Easy

14. D. Compare [40, 110, 40, 40, 100]; the minimum is 40.

APDI26-06-14 | line-charts | Easy

15. C. Add the five point labels [45, 50, 125, 45, 65]; total 330.

APDI26-06-15 | line-charts | Easy

16. B. Use Year 1=115 and Year 5=100; absolute change |100−115|=15.

APDI26-06-16 | line-charts | Medium

17. C. Year 2=115 and Year 3=115; total 230.

APDI26-06-17 | line-charts | Medium

18. B. Compare [80, 65, 105, 55, 45]; the peak is 105.

APDI26-06-18 | line-charts | Medium

19. B. Compare [40, 130, 60, 70, 90]; the minimum is 40.

APDI26-06-19 | line-charts | Medium

20. A. Add the five point labels [75, 100, 115, 90, 60]; total 440.

APDI26-06-20 | line-charts | Medium

21. C. Use Year 1=120 and Year 5=60; absolute change |60−120|=60.

APDI26-06-21 | line-charts | Medium

22. D. Year 2=110 and Year 3=130; total 240.

APDI26-06-22 | line-charts | Medium

23. B. Compare [130, 85, 125, 75, 40]; the peak is 130.

APDI26-06-23 | line-charts | Medium

24. C. Compare [115, 75, 125, 90, 100]; the minimum is 75.

APDI26-06-24 | line-charts | Medium

25. D. Add the five point labels [70, 125, 100, 130, 55]; total 480.

APDI26-06-25 | line-charts | Medium

26. D. Use Year 1=105 and Year 5=45; absolute change |45−105|=60.

APDI26-06-26 | line-charts | Medium

27. B. Year 2=95 and Year 3=65; total 160.

APDI26-06-27 | line-charts | Medium

28. D. Compare [50, 115, 70, 130, 60]; the peak is 130.

APDI26-06-28 | line-charts | Medium

29. B. Compare [45, 125, 115, 120, 65]; the minimum is 45.

APDI26-06-29 | line-charts | Medium

30. A. Add the five point labels [40, 85, 120, 130, 55]; total 430.

APDI26-06-30 | line-charts | Medium

31. C. Use Year 1=100 and Year 5=120; absolute change |120−100|=20.

APDI26-06-31 | line-charts | Medium

32. A. Year 2=70 and Year 3=40; total 110.

APDI26-06-32 | line-charts | Medium

33. A. Compare [45, 120, 125, 115, 70]; the peak is 125.

APDI26-06-33 | line-charts | Medium

34. C. Compare [115, 50, 85, 75, 75]; the minimum is 50.

APDI26-06-34 | line-charts | Medium

35. C. Add the five point labels [65, 45, 60, 80, 110]; total 360.

APDI26-06-35 | line-charts | Medium

36. A. Use Year 1=95 and Year 5=75; absolute change |75−95|=20.

APDI26-06-36 | line-charts | Medium

37. D. Year 2=100 and Year 3=70; total 170.

APDI26-06-37 | line-charts | Medium

38. C. Compare [50, 70, 45, 45, 70]; the peak is 70.

APDI26-06-38 | line-charts | Medium

39. D. Compare [125, 45, 125, 90, 80]; the minimum is 45.

APDI26-06-39 | line-charts | Medium

40. D. Add the five point labels [75, 40, 60, 75, 55]; total 305.

APDI26-06-40 | line-charts | Medium

41. A. Use Year 1=45 and Year 5=55; absolute change |55−45|=10.

APDI26-06-41 | line-charts | Difficult

42. D. Year 2=130 and Year 3=95; total 225.

APDI26-06-42 | line-charts | Difficult

43. A. Compare [105, 110, 95, 40, 115]; the peak is 115.

APDI26-06-43 | line-charts | Difficult

44. D. Compare [100, 125, 65, 115, 80]; the minimum is 65.

APDI26-06-44 | line-charts | Difficult

45. D. Add the five point labels [85, 65, 80, 115, 60]; total 405.

APDI26-06-45 | line-charts | Difficult

46. B. Use Year 1=80 and Year 5=130; absolute change |130−80|=50.

APDI26-06-46 | line-charts | Difficult

47. D. Year 2=60 and Year 3=110; total 170.

APDI26-06-47 | line-charts | Difficult

48. C. Compare [55, 80, 70, 50, 80]; the peak is 80.

APDI26-06-48 | line-charts | Difficult

49. A. Compare [120, 120, 105, 90, 130]; the minimum is 90.

APDI26-06-49 | line-charts | Difficult

50. B. Add the five point labels [45, 105, 65, 100, 75]; total 390.

APDI26-06-50 | line-charts | Difficult