Cambridge O Level Mathematics (Syllabus D) · Syllabus 4024 · Statistics
Histograms
What is Histograms?
A diagram for grouped continuous data in which the horizontal width of each bar is the class width and the vertical height is the frequency density, defined as the frequency divided by the class width. Because height multiplied by width returns the frequency, it is the area of a bar rather than its height that represents how many observations the class contains, so the tallest bar need not be the class with the greatest frequency. Adjacent bars touch because the classes are continuous and share boundaries, the vertical axis must be labelled frequency density rather than frequency, and values recorded to the nearest whole unit must first be converted to true class boundaries such as 9.5 to 19.5 for a class recorded as 10 to 19.
This definition is part of the Statistics chapter in Cambridge O Level Mathematics (Syllabus D).
Histograms in context
The classification is not a labelling exercise for its own sake — it decides what is legal downstream. Categorical data can have a mode but never a mean. Discrete data can be listed value by value. Continuous data is collected into intervals as soon as the values are many and varied, and it is that grouped continuous data which leads to cumulative-frequency curves and histograms. A short list of measurements can still be handled value by value, with an exact mean and median — see WE 9.2a in 9.2. Get this line wrong and every later step inherits the error.