Graphical representation of data

• Pictograms use a key; bar charts use bar height; pie charts use angle (360° ÷ total per item).
• Two-way tables show two categories at once; rows and columns add to totals.
• Interpret charts: read values, compare, and spot misleading features.
• Higher: histograms for unequal class widths — frequency density = frequency ÷ class width.
• Higher: cumulative frequency is plotted at the upper class boundary and joined with a smooth curve.

Picture keys and bar heights

A pictogram needs a key (for example, one symbol = 4 people); part of a symbol shows part of that amount. A bar chart has bars of equal width with gaps between them, a labelled frequency axis starting at 0, and a title. A dual (compound) bar chart puts two bars side by side to compare groups.

Angles from frequencies

Each item gets 360° ÷ (total frequency). To read a pie chart, reverse it: frequency = (angle ÷ 360) × total.

Fill in the gaps

Tally raw data into a frequency table before drawing any diagram. A two-way table shows two categories; each row and column adds up to its total. Fill the gaps using whichever row or column has only one unknown.

Area represents frequency

For continuous data with unequal class widths, the height of each bar is the frequency density, so the area of each bar is the frequency. There are no gaps between bars.

Running totals

upper class boundary