Graphical and statistical skills

A triangular graph has three axes at an angle, not one vertical axis. Each percentage is read by following the guideline PARALLEL to the correct side from its variable's axis. Reading straight up and down, like a bar chart, gives a wrong figure -- examiners note 25% read where the angled value was 15%. Trace the parallel guideline for each axis before reading off.

Naming or justifying a graph type tests the "choose the right graph" skill, and is answered poorly. For age-sex data, candidates often suggest a line or scatter graph -- which cannot show two variables either side of a central axis -- not a population pyramid. A second trap is vagueness: "pyramid" alone is not accepted for "population pyramid".

When reading a graph or table, precision is credited and vagueness is not. Saying a value is "about 200", or "the majority" when the exact figure can be read, forfeits marks an exact figure would earn. This matters most in "majority" claims about a value under 50%. Always quote the precise number with its unit (people per km2, %, mm, thousand).

When a question asks what a graph or resource SHOWS, describe the data -- its shape, values and pattern -- not its causes. Asked to read a population pyramid or trend, candidates often explain WHY (birth/death rates, migration) instead of stating what the resource displays. Save causes for an "explain" question; a "describe" mark is earned only by reporting the shown data.

The range is not a type of average. It is the highest value minus the lowest, and measures how SPREAD OUT the data is -- the gap between extremes -- not a typical or central value. Candidates sometimes quote the range where a mean or median is wanted, or confuse it with the median (the middle value). Keep them separate: range = spread; mean or median = the typical value.

An anomaly is a value that clearly breaks the pattern, and must be named and quantified SEPARATELY from the general trend. Candidates often absorb it into a vague "the figures fluctuated", losing the mark. State the overall pattern first, then flag the anomaly explicitly -- the exact year and figure -- e.g. "numbers rose steadily, but in 2020 fell to 60 thousand".

A testable wrong belief: that the mean is always the fairest "typical" average. The mean uses every value, so a single anomaly pulls it away from the typical value. The median takes the middle value once ordered, so an extreme barely affects it, making it more representative when an anomaly is present. Use the mean for evenly-spread data, the median when an anomaly exists.