0580

Cumulative Frequency

Statistics

Plotting at the upper bound

  • The single most important rule: each running total goes above the upper bound of its class, never above the midpoint
  • The reason is that only at the end of a class can every value in it be guaranteed to have been counted
  • So the table above gives the points (10, 4), (20, 15), (30, 36), (40, 52) and (50, 60)
  • Add a starting point at the lower bound of the first class with a cumulative frequency of zero, here (0, 0)
  • The syllabus asks for points to be clearly marked, for example as small crosses, and joined with a smooth curve
  • The curve has a stretched S-shape, rising steeply where the frequencies are largest, and it never turns back down
A cumulative frequency diagram for quiz times, each point marked with a cross at the upper bound of its class and the crosses joined by a smooth stretched S-shaped curve rising from 0 at 25 seconds to 50 at 55 seconds
Source: Drawing cumulative frequency diagrams by Save My Exams