Processing, representing and analysing data
Tables, charts and grouping
Raw data must be organised before it can be interpreted. Frequency tables record counts; grouped frequency tables put continuous data into class intervals, and the midpoint of each class is used later for estimates. Two-way tables show two categorical variables at once and should be read using row and column totals, not single cells.
Know the standard representations: bar charts for categorical data (gaps between bars, height = frequency); pie charts (angle = fraction × 360°); stem-and-leaf diagrams, which keep the original values and reveal shape; and histograms for continuous data, where bars touch.
Trap: in a histogram with unequal class widths, the vertical axis is frequency density = frequency ÷ class width, so it is the area of a bar, not its height, that represents frequency. In a bar chart the height always represents frequency, so never compute frequency density there. Also be careful with class boundaries: the class 10–19 covers 9.5 to 19.5, so its width is 10, not 9 and not 20. When comparing two charts, quote figures rather than saying one is 'bigger'.
Worked example. A class 20 < x ≤ 30 has frequency 24. Width = 10, so frequency density = 24 ÷ 10 = 2.4. The bar is drawn 2.4 high and 10 wide, giving area 24, which matches the frequency. To read a frequency back from any histogram bar, multiply its height by its width.