A sector is a share of a whole

A pie chart divides a whole into sectors that sum to 100% or 360 degrees. If a sector is 72 degrees, it represents 72/360=20% of the whole. If the whole is 900 units, that sector contains 180 units. Percentages printed inside the chart remove the need to use degrees. A sector's absolute quantity cannot be determined from a percentage alone unless the total is supplied or inferable.

Keep different totals separate

Two pie charts may represent different years or groups with different totals. A 25% sector in a total of 800 equals 200; a 20% sector in a total of 1,200 equals 240. Thus a smaller percentage can represent a larger quantity. When asked for growth, first convert both shares to quantities and only then compute the percent change using the earlier quantity as base. Never compare sector angles alone across unequal wholes.

Remainders and ratios

If labelled shares sum to 85%, the remaining sector is 15%. Check that categories are mutually exclusive before interpreting the remainder. For a ratio of two sectors in the same pie, the whole cancels: 30% : 20% becomes 3 : 2. For sectors from different pies, convert to quantities first. In the practice set, write the whole at the centre of your scratch circle and each required share on the rim; this prevents mixing bases.

Turn a sector into a quantity

Suppose a pie chart allocates 400 units as A 10%, B 15%, C 20%, D 25% and E 30%. A contains 40 units and E contains 120. A and B together account for 25%, or 100 units. The difference between E and C is 120−80=40 units. These are exact because the whole is given. Without the whole, the pie alone gives proportions and angles, not absolute counts.

The central angle for D is 25% of 360°, or 90°. The angle for E is 108°. Angles are another representation of share: divide an angle by 360° to recover the fraction of the whole. Do not answer a quantity question with 90 just because D's angle is 90°; its quantity is 100 units in this example. Write the requested unit next to the expression before computing.

Compare two pies with different totals

If another year has total 600 and A is 8%, A has 48 units. Its share fell from 10% to 8%, yet its quantity rose from 40 to 48. Therefore “share decreased” does not imply “count decreased” when the whole changed. Convert shares to quantities before comparing counts across different pies. If the question asks percentage-point change, subtract the percentages (8%−10%=−2 percentage points); if it asks percent change in the share, divide the 2-point fall by the original 10%, giving a 20% relative fall.

Completeness check

Shares of mutually exclusive exhaustive sectors total 100%. In the example, 10+15+20+25+30=100. If a question hides one share, subtract the visible shares from 100. For a sector angle, all angles total 360°. These totals are useful checks but do not override a note that the chart shows only selected categories. Read any “other” sector and whether the whole is a sample or a population before treating it as complete.

Practice — 50 questions

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

1. How many units are in the Unit A sector?

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

2. How many units are in Unit A and Unit B together?

A. 110 B. 105 C. 95 D. 100

3. What is the absolute difference between Unit C and Unit D?

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

4. What is the central angle in degrees of the Unit E sector?

A. 77 B. 67 C. 72 D. 82

5. How many units are outside the Unit A sector?

A. 650 B. 645 C. 635 D. 640

6. How many units are in the Unit A sector?

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

7. How many units are in Unit A and Unit B together?

A. 155 B. 160 C. 150 D. 145

8. What is the absolute difference between Unit C and Unit D?

A. 25 B. 30 C. 40 D. 35

9. What is the central angle in degrees of the Unit E sector?

A. 64 B. 54 C. 59 D. 49

10. How many units are outside the Unit A sector?

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

11. How many units are in the Unit A sector?

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

12. How many units are in Unit A and Unit B together?

A. 175 B. 190 C. 185 D. 180

13. What is the absolute difference between Unit C and Unit D?

A. 30 B. 35 C. 40 D. 25

14. What is the central angle in degrees of the Unit E sector?

A. 64 B. 59 C. 54 D. 49

15. How many units are outside the Unit A sector?

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

16. How many units are in the Unit A sector?

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

17. How many units are in Unit A and Unit B together?

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

18. What is the absolute difference between Unit C and Unit D?

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

19. What is the central angle in degrees of the Unit E sector?

A. 113 B. 103 C. 118 D. 108

20. How many units are outside the Unit A sector?

A. 720 B. 730 C. 725 D. 715

21. How many units are in the Unit A sector?

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

22. How many units are in Unit A and Unit B together?

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

23. What is the absolute difference between Unit C and Unit D?

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

24. What is the central angle in degrees of the Unit E sector?

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

25. How many units are outside the Unit A sector?

A. 690 B. 675 C. 680 D. 685

26. How many units are in the Unit A sector?

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

27. How many units are in Unit A and Unit B together?

A. 305 B. 310 C. 295 D. 300

28. What is the absolute difference between Unit C and Unit D?

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

29. What is the central angle in degrees of the Unit E sector?

A. 103 B. 108 C. 118 D. 113

30. How many units are outside the Unit A sector?

A. 330 B. 325 C. 320 D. 315

31. How many units are in the Unit A sector?

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

32. How many units are in Unit A and Unit B together?

A. 285 B. 280 C. 275 D. 290

33. What is the absolute difference between Unit C and Unit D?

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

34. What is the central angle in degrees of the Unit E sector?

A. 41 B. 46 C. 36 D. 31

35. How many units are outside the Unit A sector?

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

36. How many units are in the Unit A sector?

A. 100 B. 95 C. 110 D. 105

37. How many units are in Unit A and Unit B together?

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

38. What is the absolute difference between Unit C and Unit D?

A. 25 B. 35 C. 30 D. 40

39. What is the central angle in degrees of the Unit E sector?

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

40. How many units are outside the Unit A sector?

A. 320 B. 325 C. 315 D. 330

41. How many units are in the Unit A sector?

A. 125 B. 130 C. 115 D. 120

42. How many units are in Unit A and Unit B together?

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

43. What is the absolute difference between Unit C and Unit D?

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

44. What is the central angle in degrees of the Unit E sector?

A. 72 B. 82 C. 77 D. 67

45. How many units are outside the Unit A sector?

A. 505 B. 520 C. 515 D. 510

46. How many units are in the Unit A sector?

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

47. How many units are in Unit A and Unit B together?

A. 275 B. 280 C. 285 D. 290

48. What is the absolute difference between Unit C and Unit D?

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

49. What is the central angle in degrees of the Unit E sector?

A. 46 B. 36 C. 31 D. 41

50. How many units are outside the Unit A sector?

A. 190 B. 185 C. 175 D. 180

Answers and explanations

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

1. B. Unit A has 20% of 400; 400×20/100=80 units.

APDI26-07-01 | pie-charts | Easy

2. D. Add their sector quantities: 40+60=100.

APDI26-07-02 | pie-charts | Easy

3. C. Unit C=30, D=20; absolute difference 10.

APDI26-07-03 | pie-charts | Easy

4. C. Unit E is 20% of a 360° circle; angle 72°.

APDI26-07-04 | pie-charts | Easy

5. D. Total 800 minus Unit A 160 gives 640.

APDI26-07-05 | pie-charts | Easy

6. D. Unit A has 10% of 800; 800×10/100=80 units.

APDI26-07-06 | pie-charts | Easy

7. C. Add their sector quantities: 90+60=150.

APDI26-07-07 | pie-charts | Easy

8. B. Unit C=90, D=60; absolute difference 30.

APDI26-07-08 | pie-charts | Easy

9. B. Unit E is 15% of a 360° circle; angle 54°.

APDI26-07-09 | pie-charts | Easy

10. B. Total 600 minus Unit A 120 gives 480.

APDI26-07-10 | pie-charts | Easy

11. C. Unit A has 25% of 200; 200×25/100=50 units.

APDI26-07-11 | pie-charts | Easy

12. D. Add their sector quantities: 120+60=180.

APDI26-07-12 | pie-charts | Easy

13. A. Unit C=150, D=180; absolute difference 30.

APDI26-07-13 | pie-charts | Easy

14. C. Unit E is 15% of a 360° circle; angle 54°.

APDI26-07-14 | pie-charts | Easy

15. A. Total 200 minus Unit A 60 gives 140.

APDI26-07-15 | pie-charts | Easy

16. D. Unit A has 30% of 200; 200×30/100=60 units.

APDI26-07-16 | pie-charts | Medium

17. C. Add their sector quantities: 60+20=80.

APDI26-07-17 | pie-charts | Medium

18. D. Unit C=200, D=120; absolute difference 80.

APDI26-07-18 | pie-charts | Medium

19. D. Unit E is 30% of a 360° circle; angle 108°.

APDI26-07-19 | pie-charts | Medium

20. A. Total 800 minus Unit A 80 gives 720.

APDI26-07-20 | pie-charts | Medium

21. A. Unit A has 20% of 200; 200×20/100=40 units.

APDI26-07-21 | pie-charts | Medium

22. A. Add their sector quantities: 240+120=360.

APDI26-07-22 | pie-charts | Medium

23. D. Unit C=120, D=100; absolute difference 20.

APDI26-07-23 | pie-charts | Medium

24. D. Unit E is 25% of a 360° circle; angle 90°.

APDI26-07-24 | pie-charts | Medium

25. C. Total 800 minus Unit A 120 gives 680.

APDI26-07-25 | pie-charts | Medium

26. C. Unit A has 20% of 200; 200×20/100=40 units.

APDI26-07-26 | pie-charts | Medium

27. D. Add their sector quantities: 120+180=300.

APDI26-07-27 | pie-charts | Medium

28. C. Unit C=80, D=120; absolute difference 40.

APDI26-07-28 | pie-charts | Medium

29. B. Unit E is 30% of a 360° circle; angle 108°.

APDI26-07-29 | pie-charts | Medium

30. C. Total 400 minus Unit A 80 gives 320.

APDI26-07-30 | pie-charts | Medium

31. B. Unit A has 25% of 200; 200×25/100=50 units.

APDI26-07-31 | pie-charts | Medium

32. B. Add their sector quantities: 120+160=280.

APDI26-07-32 | pie-charts | Medium

33. B. Unit C=40, D=100; absolute difference 60.

APDI26-07-33 | pie-charts | Medium

34. C. Unit E is 10% of a 360° circle; angle 36°.

APDI26-07-34 | pie-charts | Medium

35. A. Total 200 minus Unit A 30 gives 170.

APDI26-07-35 | pie-charts | Medium

36. A. Unit A has 25% of 400; 400×25/100=100 units.

APDI26-07-36 | pie-charts | Medium

37. B. Add their sector quantities: 30+50=80.

APDI26-07-37 | pie-charts | Medium

38. C. Unit C=90, D=120; absolute difference 30.

APDI26-07-38 | pie-charts | Medium

39. C. Unit E is 25% of a 360° circle; angle 90°.

APDI26-07-39 | pie-charts | Medium

40. A. Total 400 minus Unit A 80 gives 320.

APDI26-07-40 | pie-charts | Medium

41. D. Unit A has 15% of 800; 800×15/100=120 units.

APDI26-07-41 | pie-charts | Difficult

42. A. Add their sector quantities: 20+40=60.

APDI26-07-42 | pie-charts | Difficult

43. A. Unit C=160, D=200; absolute difference 40.

APDI26-07-43 | pie-charts | Difficult

44. A. Unit E is 20% of a 360° circle; angle 72°.

APDI26-07-44 | pie-charts | Difficult

45. D. Total 600 minus Unit A 90 gives 510.

APDI26-07-45 | pie-charts | Difficult

46. A. Unit A has 10% of 600; 600×10/100=60 units.

APDI26-07-46 | pie-charts | Difficult

47. B. Add their sector quantities: 80+200=280.

APDI26-07-47 | pie-charts | Difficult

48. C. Unit C=30, D=50; absolute difference 20.

APDI26-07-48 | pie-charts | Difficult

49. B. Unit E is 10% of a 360° circle; angle 36°.

APDI26-07-49 | pie-charts | Difficult

50. D. Total 200 minus Unit A 20 gives 180.

APDI26-07-50 | pie-charts | Difficult