Histograms and Scatter Graphs (Extended)

Beyond Basic Graphs

At Extended level, histogram and scatter graph work moves beyond simple reading and plotting. You are expected to construct and interpret more sophisticated graphical representations, handle grouped data with unequal class widths, and extract precise information from complex displays.

Grouped Frequency Histograms

Unlike bar charts, histograms display continuous data with no gaps between bars. When class widths are unequal, the height of each bar is the frequency density, not the frequency:

Frequency Density = Frequency ÷ Class Width

This ensures that the area of each bar represents the frequency, not the height. A common mistake is to read the y-axis as frequency when class widths differ — always check the axis label.

Key Skills

• Calculating frequency density from a grouped frequency table
• Drawing histograms with correctly scaled frequency density axes
• Estimating frequencies from a histogram where class widths vary

Reading Complex Scatter Graphs

Extended scatter graph questions often include additional features: multiple datasets on one graph, labelled subgroups, or outliers that require commentary. You should be able to:

• Compare trends across two groups plotted on the same axes
• Identify and discuss anomalous data points
• Link graphical observations to the real-world context described

Common Mistakes

• Using frequency rather than frequency density on the y-axis of a histogram with unequal class widths
• Calculating area incorrectly by using midpoints instead of class boundaries
• Failing to comment on outliers when they are clearly visible

Criterion D Connection

Histograms and scatter graphs appear frequently in Criterion D tasks set in contexts such as population data, environmental measurement, or health statistics. Practice reading unfamiliar graphs quickly and forming conclusions in context.