Presentation of Data

Presenting data in text, tables and diagrams: the parts of a table, bar and pie diagrams, histograms, frequency polygons, ogives and line graphs.

Key ideas

Data can be presented in text (small data), tables (compact and exact) or diagrams (quick and attractive).
A table has a number, title, captions (column headings), stubs (row headings), body, unit, source and note.
Simple bar diagrams compare one set of figures; multiple bars put sets side by side; component bars split a total into parts.
A pie diagram shows the shares of a whole as sectors of a circle.
A histogram has touching rectangles on class intervals, and their areas stand for the frequencies; joining the mid-points of their tops gives a frequency polygon.
Ogives are cumulative frequency curves: the less than ogive rises, the more than ogive falls, and they cross at the median.
An arithmetic line graph shows a time series and its trend.

Pie sector angle	part ÷ total × 360° (or per cent × 3.6)
Per cent from an angle	angle ÷ 360 × 100
Histogram height (unequal classes)	frequency × standard width ÷ class width
Less than ogive	plot cumulative frequency against each UPPER limit
More than ogive	add from the bottom class upward; plot against each LOWER limit
Frequency polygon	plot (class mark, frequency) and join the points
Percentage change	(new − old) ÷ old × 100

Leaving gaps between histogram rectangles, or drawing a histogram for discrete data.
Using the frequency as the height of a wider class without adjusting it.
Forgetting to multiply the share by 360° for a pie diagram.

Write the points of the more than ogive (lower limit, cumulative frequency) for:
Class: 60–80, 80–100, 100–120, 120–140
Frequency: 17, 6, 17, 30

Working: add the frequencies from the bottom class upwards

Answer: (60, 70), (80, 53), (100, 47), (120, 30)