This deep dive covers Finding Quartiles within Cumulative Frequency for GCSE Mathematics. Revise Cumulative Frequency in Statistics for GCSE Mathematics with 14 exam-style questions and 20 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 7 of 11 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Finding Quartiles
Quartile Positions
- Q1 (Lower Quartile): Position = n ÷ 4
- Q2 (Median): Position = n ÷ 2
- Q3 (Upper Quartile): Position = 3n ÷ 4
Example with n = 43
Q1 position: 43 ÷ 4 = 10.75 → Q1 ≈ 168 cm
Q2 position: 43 ÷ 2 = 21.5 → Q2 ≈ 175 cm
Q3 position: 3 × 43 ÷ 4 = 32.25 → Q3 ≈ 181 cm
IQR: Q3 - Q1 = 181 - 168 = 13 cm
Q2 position: 43 ÷ 2 = 21.5 → Q2 ≈ 175 cm
Q3 position: 3 × 43 ÷ 4 = 32.25 → Q3 ≈ 181 cm
IQR: Q3 - Q1 = 181 - 168 = 13 cm
Practice questions for Cumulative Frequency
Cumulative frequency is:
The graph shows the times for 60 students. The cumulative frequency at 40 seconds reads as 48. Estimate the number of students who took longer than 40 seconds to complete the puzzle.
Quick recall flashcards
What is cumulative frequency?
Cumulative frequency is the running total of frequencies up to and including each class. It shows how many data values fall below the upper boundary of each class.
How do you calculate cumulative frequency?
Start with the first frequency. For each subsequent class, add the current frequency to the previous cumulative frequency:
CF₂ = CF₁ + f₂
CF₃ = CF₂ + f₃, and so on.