CAIE A-Level Mathematics 5.1.4 Cumulative Frequency Graphs

Practise reading cumulative-frequency graphs to estimate medians, quartiles, percentiles and numbers above or below a value by converting each request into a cumulative rank.

Exam points

convert a median, quartile or percentile request into the corresponding cumulative frequency
read the data value from the curve at a target rank using consistent horizontal and vertical guides
subtract cumulative readings from the total or from each other to estimate interval frequencies

[Maximum number: 1]

The times, t minutes, taken to complete a walking challenge by 250 members of a club are summarised in the table.

Table for Question 5.1.4—A cumulative frequency graph e question 1 — CAIE A-Level Mathematics AS

Use your graph to estimate the 60th percentile of the data.

Line drawn from 150 on cf axis to meet graph at about
t=38 minutes

B1 FT

Must be an increasing cf graph with correct upper bounds.
Use of graph must be seen.
Expect an answer in range $37 \leqslant t \leqslant 39$ for a correct graph

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5.1.4—A cumulative frequency graph e question 1