Introduction
A cumulative frequency graph (also called an ogive) is one of the most frequently tested tools in the Probability & Statistics 1 paper. Where a histogram shows the distribution of data, a cumulative frequency graph lets you read off summary statistics — medians, quartiles, percentiles — directly from a curve, and estimate the proportion of data lying above, below, or between any two values. Expect to both draw one from a table and extract several values from one in the same question.
Core Concept
Cumulative frequency is the running total of frequencies up to (and including) each class. For grouped continuous data, the cumulative frequency at any point is the total number of data values less than or equal to .
Building the table
Starting from a frequency table, add a column of cumulative frequencies. Each entry is the sum of all frequencies up to and including that class.
Plotting the graph
- Plot each cumulative frequency at the upper class boundary of its class (not the midpoint).
- The first point plotted at the lower boundary of the first class has cumulative frequency 0.
- Join the points with a smooth curve (the ogive). For exam questions "draw a smooth curve through the points" scores the mark.
Reading off estimates
Once drawn, use the graph by:
- Going across from a cumulative frequency value on the -axis to the curve, then down to the -axis — this gives a data value (e.g. median, quartile).
- Going up from an -axis value to the curve, then across to the -axis — this gives a cumulative frequency, from which you calculate a proportion.
Unlock the full Representation of Data note with Nova
You're reading the preview. Unlock the complete note — every worked example, examiner pitfall and practice question — plus 24/7 AI tutoring from Nova that teaches directly from these notes.