A pie chart (or a circle chart) is a circular statistical graphic divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice (and consequently its central angle and area) is proportional to the quantity it represents. It is widely used in data handling to compare parts of a whole.
Essential Formulas
To solve pie chart problems accurately, use the following standard formulas:
Answer the following 10 practice questions based on standard JAMB evaluation metrics.
Question 1: In a pie chart representing the expenditure of a student, the total amount spent was $18,000. If the sector for books has an angle of 60°, how much was spent on books?
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Explanation: Fraction of the circle = 60⁄360 = 1⁄6.
Amount spent on books = 1⁄6 × $18,000 = $3,000.
Question 2: The grades of a group of students in a test are represented on a pie chart. If the sector angles for grades A, B, and C are 90°, 120°, and 100° respectively, and the rest obtained grade D, what is the sector angle for grade D?
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Explanation: Total sum of angles in a circle is 360°.
90° + 120° + 100° + D = 360° ⇒ 310° + D = 360° ⇒ D = 50°.
Question 3: A pie chart shows the distribution of crops on a farm. The sector angle for Cocoa is 144°. What percentage of the total farm produce is Cocoa?
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Explanation: Percentage = (144⁄360) × 100% = 0.4 × 100% = 40%.
Question 4: The distribution of 720 students in a school according to their favorite sports is represented on a pie chart. If the sector angle for Football is 105°, how many students prefer Football?
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Explanation: Number of students = (105⁄360) × 720.
Since 720 ÷ 360 = 2, it simplifies to: 105 × 2 = 210 students.
Question 5: A budget distribution pie chart allocates 160° for Salaries and 80° for Infrastructure. If the amount spent on Infrastructure is $4,000,000, how much is spent on Salaries?
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Explanation: The angle for Salaries (160°) is exactly double the angle for Infrastructure (80°). Therefore, the budget scales proportionally: 2 × $4,000,000 = $8,000,000.
Question 6: A pie chart is used to show the population of four villages A, B, C, and D. The ratio of their populations is 2:3:4:3 respectively. What is the sector angle representing village C?
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Explanation: Total ratio parts = 2 + 3 + 4 + 3 = 12. Village C's fraction = 4⁄12 = 1⁄3.
Sector angle = 1⁄3 × 360° = 120°.
Question 7: The transport choices of employees in a company are shown on a pie chart. If 15% of employees walk to work, what is the size of the sector angle that represents this group?
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Explanation: Angle = 15% of 360° = (15⁄100) × 360 = 54°.
Question 8: In a pie chart, a sector representing 24 items has an angle of 72°. Find the total number of items represented by the entire pie chart.
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Explanation: Fraction of the chart = 72⁄360 = 1⁄5.
If 1⁄5 of the total = 24 items, then Total = 24 × 5 = 120 items.
Question 9: A monthly family income is spent as follows: Food (135°), Rent (90°), Education (x°), and Savings (60°). If the family saves $15,000 monthly, what is the angle x° allocated for Education?
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Explanation: The total degrees must equal 360°.
135° + 90° + x° + 60° = 360° ⇒ 285° + x° = 360° ⇒ x = 75°. (The money figure is extra context).
Question 10: If a pie chart sector with an angle of 45° represents a frequency of 15, what is the frequency represented by a sector with an angle of 120°?
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Explanation: Frequency per degree = 15⁄45 = 1⁄3.
Frequency for a 120° sector = 120 × 1⁄3 = 40.