CIE iGCSE Maths E9.6 Cumulative frequency diagrams Exam Style Practice Questions- Paper 2
The time taken for each of 200 students to complete a calculation is measured. The cumulative frequency diagram shows the results.
Use the diagram to find an estimate for:
(a) the interquartile range
(b) the number of students taking more than 40 seconds to complete the calculation.
▶️ Answer/Explanation
(a) Ans: 11 seconds
Calculating Interquartile Range (IQR):
- Total students = 200
- Lower quartile (Q₁) position = 25% of 200 = 50th student
- Upper quartile (Q₃) position = 75% of 200 = 150th student
- From graph:
- Q₁ ≈ 16 seconds (when CF = 50)
- Q₃ ≈ 27 seconds (when CF = 150)
- IQR = Q₃ – Q₁ = 27 – 16 = 11 seconds
(b) Ans: 6 students
Finding students taking >40 seconds:
- At 40 seconds, cumulative frequency ≈ 194
- Students taking >40s = Total – CF at 40s = 200 – 194 = 6
Key points to remember:
- IQR measures the middle 50% of data (Q₃ – Q₁)
- Cumulative frequency graphs show running totals
- For “more than” questions, subtract from total
The speed-time graph shows information about a car journey.
(a) Find the deceleration of the car between 240 and 320 seconds.
(b) Calculate the total distance the car travels during the 320 seconds.
▶️ Answer/Explanation
(a) Ans: 0.2 m/s²
Deceleration = \(\frac{\text{Change in speed}}{\text{Time}}\)
From graph:
• Speed decreases from 16 m/s to 0 m/s
• Time interval = 320 – 240 = 80 s
\(\text{Deceleration} = \frac{16 – 0}{80} = 0.2 \, \text{m/s}^2\)
(b) Ans: 4240 m
Total distance = Area under graph (3 parts):
- 0-30s (Triangle): \(\frac{1}{2} × 30 × 16 = 240 \, \text{m}\)
- 30-240s (Rectangle): \(210 × 16 = 3360 \, \text{m}\)
- 240-320s (Triangle): \(\frac{1}{2} × 80 × 16 = 640 \, \text{m}\)
Total distance = \(240 + 3360 + 640 = 4240 \, \text{m}\)