GCSE Maths revision · Higher: probability and statistics
Cumulative frequency is a running total. Plot each total at the upper end of its class and join with a smooth curve. Read the median at half the total, and the quartiles at a quarter and three quarters.
Watch out Plot at the end of each class, not the middle.
The table shows information about the marks of 80 students in a test.
| Mark (m) | Frequency |
|---|---|
| 0 < m ≤ 20 | 4 |
| 20 < m ≤ 40 | 10 |
| 40 < m ≤ 60 | 26 |
| 60 < m ≤ 80 | 30 |
| 80 < m ≤ 100 | 10 |
(a) Work out the cumulative frequency for marks up to 60.
(b) Write down the coordinates of the point plotted for the class on a cumulative frequency graph.
Answer (a) 40; (b)
The cumulative frequency graph shows information about the waiting times of 80 people.
Use the graph to find an estimate for the number of people who waited more than 25 minutes.
The cumulative frequency graph shows information about 120 processing times.
Use cumulative frequencies 30 and 90 for the lower and upper quartiles.
A new process changes every time according to .
Use the graph to estimate the interquartile range of the new times. Give your answer to 1 decimal place.
The cumulative frequency graph shows information about the heights of 60 plants.
(a) Use the graph to find an estimate for the median height.
(b) Use the graph to estimate the number of plants taller than 35 cm.
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